What is claimed is;

wherein R³-R⁸, X, and Y have the values defined in a), b), or c) below:

a) X is N; Y is C(R²); and R³ is R^e; or

X is N; Y is C(R¹⁵); and R³ is R^c; or

X is C(R'); Y is N; and R³ is R^c or

X is C(R¹⁶); Y is C(R^U); and R³ is R^e ; or

X is C(R'); Y is C(R'²); and R³ is R^e ; or

X is C(R³⁰); Y is C(R³¹); and R³ is R^e ; or

X is N⁺- R¹³ (Z ); Y is C(R¹²); and R³ is R^c ; or

X is N; Y is C(R¹²); and R³ is R^e or

X is C(R¹⁰) or C(R³¹); Y is N⁺-R¹⁴ (Z ); and R³ is R^c; or

X is C(R¹⁰) or C(R³¹); Y is N; and R³ is R^c;

R¹ is R^y or (C] -C6)alkyl that is substituted with one or more R^y;

R² is R^z or (Ci-C6)alkyl that is substituted with one or more R^x;

at least one of R⁴, R⁵, R⁶, R⁷, R⁸, and R³¹ is aryl or heteroaryl wherein each aryl or heteroaryl is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^d; and the remainder of R⁴, R⁵, R⁶, R⁷, and R⁸ are each independently H, halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (Ci-C₆)alkyl, (C₃-C6)cycloalkyl, (C_rC6)alkoxy, (Q- Ce)alkoxycarbonyl, (Ci-Ce)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, (C\- C₆)alkylthio, -S(0)R^p, -S(0)₂R^p, -S(0)₃R^p, -S(0)₂NR^gR^h, and -NR^gR^h; wherein any alkyl is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^a ; and any remaining R³¹ is -C(=NR^hb)-NR^hcR^hd, -NR^he-C(=NR^hb)-NR^hcR^hd, -NR^ke-C(=NR^kb)R^ke, or (C,-C₆)alkyl which is substituted with one or more groups selected from -C(=NR^hb)-NR^hcR^hd, -NR^he-C(=NR^hb)- NR^hcR^hd, and -NR^ke-C(=NR^kb)R^ke; wherein any aryl, or heteroaryl of R⁴, R⁵, R⁶, R⁷, R⁸, and R³¹ is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^b; each R is H, halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, (Ci-C₆)alkoxy, (Ci-C₆)alkoxycarbonyl, (Ci-C₆)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, and -NR^gR^h; wherein any alkyl of R¹⁰ is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^a ; and wherein any aryl, heteroaryl, or any aryl or heteroaryl portion of any aryl(C₁-C6)alkyl, heteroaryl(Ci-C6)alkyl, aryloxy, or heteroaryloxy of R¹⁰ is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^b;

each R¹¹ is H, halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, (Ci-C₆)alkoxy, (Ci-C₆)alkoxycarbonyl, (Ci-C₆)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, and -NR^gR^h; wherein any alkyl and any alkyl or alkanoyl portion of any aryl(C]-C₆)alkyl, heteroaryl(Ci-C₆)alkyl, aryl(d-C₆)alkanoyl or heteroaryl(C]-C6)alkanoyl of R^u is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^a ; and wherein any aryl, heteroaryl, or any aryl or heteroaryl portion of any aryl(Ci-C6)alkyl, heteroaryl(Ci-C6)alkyl, aryl(Ci-C₆)alkanoyl or heteroaryl(Ci-C6)alkanoyl of R¹¹ is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^b;

each R¹² is H, halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, (C]-C₆)alkoxy, (Ci-C₆)alkoxycarbonyl, (Ci-C₆)alkanoyloxy, aryloxy, heteroaryloxy, and -NR^gR^h; wherein any alkyl and any alkyl or alkanoyl portion of any aryl(Ci-C₆)alkyl, heteroaryl(C,-C₆)alkyl, aryl(d-C₆)alkanoyl or heteroaryl(Ci-C₆)alkanoyl of R¹² is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^a ; and wherein any aryl, heteroaryl, or any aryl or heteroaryl portion of any aryl(Ci-C₆)alkyl, heteroaryl(Ci-C6)alkyl, aryl(CrC6)alkanoyl or heteroaryl(C]-C6)alkanoyl of R¹² is optionally substituted with one or more (e.g. 1 , 2, 3, or 4) R^b;

each R¹³ is (Q-Ce^lkyl, aryl, or aryl(C C₆)alkyl;

each R¹⁴ is (C C₆)alkyl, aryl, or aryl(C C₆)alkyl;

R¹⁵ is R^x or (C_t-C6)alkyl that is substituted with one or more R^x;

R¹⁶ is R^z or (d-CeJalkyl that is substituted with one or more R^y;

each R³⁰ is H or (CrC₆)alkyl,

each R^a is independently selected from halo, cyano, nitro, hydroxy, carboxy, oxo, (Cj- C6)alkyl, (C3-C6)cycloalkyl, (C]-C6)alkoxy, (Ci-C6)alkoxycarbonyl, (Ci-C6)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, (C C₆)alkylthio, -S(0)R^p, -S(0)₂R^p, -S(0)₃R^p, -S(0)₂NR^gR^h, and -NR^gR^h; wherein each aryl, heteroaryl, aryloxy, and heteroaryloxy is optionally substituted with one or more (e.g. 1, 2, 3, or 4) groups independently selected from halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (Ci-C₆)alkyl, (C₃-C6)cycIoalkyI, (Ci- C₆)alkoxy, (C,-C₆)a]koxycarbonyl, (C_rC₆)alkanoyloxy, (C,-C₆)a]kylthio, -S(0)R^p, -S(0)₂R^p, -S(0)₃R^p, -S(0)₂NR^gR^h, and -NR^gR^h;

each R^b is independently selected from halo, cyano, nitro, hydroxy, carboxy,

trifluoromethyl, trifluoromethoxy, (C] -C6)alkyl, (C₃-C6)cycloalkyl, (Ci-C₆)alkoxy, (C

C₆)alkoxycarbonyl, (Ci-C6)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, (Ci- C₆)alkylthio, -S(0)R^p, -S(0)₂R^p, -S(0)₃R^p, -S(0)₂NR^gR^h, and -NR^gR^h; wherein each aryl, heteroaryl, aryloxy, and heteroaryloxy is optionally substituted with one or more (e.g. 1 , 2, 3, or 4) groups independently selected from halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (Ci-C6)alkyl, (C₃-C₆)cycloalkyl, (Ci-C6)alkoxy, (Ci-C6)alkoxycarbonyl, (Cp C₆)alkanoyloxy, (d-C₆)alkylthio, -S(0)R , -S(0)₂R^p, -S(0)₃R^p, -S(0)₂NR⁸R^h, and -NR^gR^b; each R^c is H, halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (Ci-C₆)alkyl, (C₃-C6)cycloalkyl, (Ci-C6)alkoxy, (Ci-C₆)alkoxycarbonyl, (Ci-C6)alkanoyloxy, aryl other than phenyl, heteroaryl other than pyrid-4-yl, aryloxy, heteroaryloxy, and -NR⁸R^h; wherein any alkyl and any alkyl or alkanoyl portion of any aryl(CrC6)alkyl, heteroaryl(Ci-C6)alkyl, aryl(Ci-C6)alkanoyl or heteroaryl(Ci-C₆)alkanoyl of R^c is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^a ; and wherein any aryl, heteroaryl, or any aryl or heteroaryl portion of any aryl(Ci-C6)alkyl, heteroaryl(Ci-C6)alkyl, aryl(C]-C6)alkanoyl or heteroaryl(C₁-C₆)alkanoyl of R^c is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^b;

each R^d is independently selected from halo, cyano, nitro, hydroxy, carboxy,

trifluoromethyl, trifluoromethoxy, (Ci-C6)alkyl, (C₃-C₆)cycloalkyl, (Ci-C₆)alkoxy, (Q- C₆)alkoxycarbonyl, (Ci-C6)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, and -NR^gR^h; wherein each aryl, heteroaryl, aryloxy, and heteroaryloxy is optionally substituted with one or more (e.g. 1, 2, 3, or 4) groups independently selected from halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, (Ci-C₆)alkoxy, (Q- C6)alkoxycarbonyl, (Ci-Ce)alkanoyloxy, and -NR⁸R^h;

each R^e is H, halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (Ci-C₆)alkyl, (C₃-C6)cycloalkyl, (Cj-C6)alkoxy, (C C6)alkoxycarbonyl, (Ci-C6)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, and -NR^gR^h; wherein any alkyl and any alkyl or alkanoyl portion of any aryl(Ci-C6)alkyl, heteroaryl(Ci-C6)alkyl, aryl(Ci-C6)alkanoyl or heteroaryl(Ci-Ce)alkanoyl of R^e is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^a ; and wherein any aryl, heteroaryl, or any aryl or heteroaryl portion of any aryl(C]-C6)alkyl, heteroaryl(Ci-C6)alkyl, aryl(Ci-C6)alkanoyl or heteroaryl(Ci-C6)alkanoyl of R^e is optionally substituted with one or more (e.g. 1 , 2, 3, or 4) R^b;

each R^g and R^h is independently selected from H, (Ci-C₆)alkyl, (C₃-Ce)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl(Ci-C₆) alkyl; or R^E and R^H together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; wherein any (Ci-Ce)alkyl, (C₃-C6)cycloalkyl, (C₃-C₆)cycloalkyl(C_rC₆)alkyl, aryl, heteroaryl, aryl(C,-C₆) alkyl or heteroaryl(d-C₆)alkyl of R^G and R^H is optionally substituted with one or more groups independently selected from hydroxy, carboxy, and NR^LR^U;

each R^J is independently selected from H, (Ci-C6)alkyl, (C₃-C₆)cycloalkyl, (C₃- C6)cycloalkyl(C)-C6)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl(Ci-Ce)alkyl;

each R^M and R^N is independently selected from H, (Ci-C₆)alkyl, (C₃-C6)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(C C₆) alkyl and heteroaryl(C_rC₆) alkyl; or R^M and R" together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; wherein any (Ci-C₆)alkyl, (C₃-C6)cycloalkyl, (C₃-C₆)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(Ci-C6) alkyl or heteroaryl(d-C₆) alkyl of R^M and R" is optionally substituted with one or more groups independently selected from hydroxy, carboxy, and NR'R^U;

each R^P is independently selected from H, (C)-C6)alkyl, (C₃-C6)cycloalkyl, (C₃- C6)cycloalkyl(C]-C₆)alkyl, aryl, heteroaryl, aryl(Ci-C6) alkyl and heteroaryl(Ci-C₆) alkyl;

each R^Q is independently selected from H, (C]-C6)alkyl, (C₃-C6)cycloalkyl, (C3- C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl(Ci-C6)alkyl;

each R^S is independently selected from H, (Ci-C6)alkyl, (C₃-C6)cycloalkyl, (C₃- C6)cycloalkyl(C]-C6)alkyl, aryl, heteroaryl, aryl(C]-C₆) alkyl and heteroaryl(Ci-C6)alkyl;

each R^L and R^U is independently selected from H, (C(-C6)alkyl, (C₃-C₆)cycloalkyl, (C₃- C6)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl(Ci-C6) alkyl; or R'and R^U together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino;

each R^X is independently -NR^MR", -N* (R^S)₃ Z\ -C(=NR^J)-NR^MR", or -NR^q-C(=NR^J)- NR^MR^N;

each R^Y is independently -NR^MR^N, -N⁺(R^S)₃ Z , -C(=NR^J)-NR^MR^N, or -NR^q-C(=NR^J)- NR^MR^N;

each R^Z is independently -C(=NR^J)-NR^MR^N, or -NR^q-C(=NR^I)-NR^MR";

each R^HB is independently selected from H, (Ci-C6)alkyl, (C₃-C6)cycloalkyl, (C₃- C6)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(Ci-C6) alkyl and heteroaryl(Ci-C6)alkyl;

each R^HC and R^HD is independently selected from H, (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(C C₆) alkyl and heteroaryl(Cj-C₆) alkyl; or R^HC and R together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; wherein any (Ci-C6)alkyl, (C₃-C6)cycloalkyl, (C₃-C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, ary](Ci-C₆) alkyl or heteroary](C,-C₆)alkyl of R^hc and R^hd is optionally substituted with one or more groups independently selected from hydroxy, carboxy, and NR^hmR^hn;

each R^he is independently selected from H, (C)-C6)alkyl, (C3-C6)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl(Ci-C₆)alkyl;

each R^hm and R^hn is independently selected from H, (C C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(C C₆) alkyl and heteroaryl(C,-C₆) alkyl; or R^hm and R^hn together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino;

each R^kb is independently selected from H, (Ci-C6)alkyl, (C3-C₆)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl(Ci-C6)alkyl;

each R^ke is independently selected from H, (Ci-C6)alkyl, (C₃-C₆)cycloalkyl, (C₃- C6)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(C]-C6) alkyl and heteroaryl(Ci-C₆)alkyl;

the bond represented by— is present; and

each Z^" is independently an acceptable counterion;

b) wherein:

X is W-R⁵¹;

Y is C(R⁵²);

W is N; R⁵¹ is absent; or

W is N⁺ D^"; R⁵¹ is (C C₆)alkyl, aryl, or aryl(C,-C₆)alkyl; or

W is C; R⁵¹ is hydrogen, -N⁺(R^5a)₃ D^", -C(=NR^5b)-NR^ScR^5d, -NR^5e-C(=NR^5b)-NR^5cR^5d, -NR⁵⁶R^5h, -NR^5ce-C(=NR^5cb)R^5ce, -NR^5ce-C(=0)-NR^5ccR^5cd, or (C,-C₆)alkyl that is substituted with one or more R^5f;

R⁵² is a ring selected from phenyl, pyridyl, and [D^" N⁺-(Ci-C6)alkylpyridyl], which ring is optionally substituted with one or more groups selected from methylenedioxy, Z-R^5x, R^5f, R^5da, and (C] -C6)alkyl that is substituted with one or more R^5f; and which ring is also optionally substituted with a group R⁶ , at a position ortho to the position where R⁵² connects with the remainder of formula I;

6 7 6 7

R and R taken together can be methylenedioxy or each R and R is independently selected from H, Z-R ^x, R^5f, and (C]-C6)alkyl that is substituted with one or more R^5f;

R⁸ is hydrogen, (Ci-Ce)alkyl, aryl, or aryl(Ci-Ce)alkyl wherein each (Ci-C6)alkyl of R⁸ is optionally substituted with one or more groups independently selected from halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, (C₃-C₆)cycloalkyI, oxo, carboxy, aryloxy, sulfo, and -NR^5gR^5h, and wherein each aryl of R⁸ is optionally substituted with one or more groups independently selected from (Ci-Ce)alkyl, halo, hydroxy, cyano, nitro, (C]-C6)alkoxy, (C3-C6)cycloalkyl, carboxy, aryloxy, nitro, R^5s, and -NR^5gR^5h;

each Z is independently selected from -0-, -S-, and -N(R^5y)-;

at least one of R³, R⁴, R⁵, and R⁶ is selected from hydroxy, carboxy, cyano, CF₃SO₃-, (C,-C₆)alkyl, (C₂-C₆)alkenyl, (C₂-C₆)alkynyl, (C_rC₆)alkoxy, (C₃-C₆)cycloalkyl, aryl(C_rC₆)alkyl, aryl, heteroaryl, heteroaryl(Ci-C₆)alkyl, aryl(Ci-C₆)alkanoyl, and heteroaryI(C]-C6)alkanoyl; and the remainder of R³, R⁴, R⁵, and R⁶ are independently selected from H, hydroxy, carboxy, cyano, CF₃SO₃-, (C_rC₆)alkyl, (C₂-C₆)alkenyl, (C₂-C₆)alkynyl, (C_rC₆)alkoxy, (C₃-C₆)cycloalkyl, aryl(Ci-C6)alkyl, aryl, heteroaryl, heteroaryl(C]-C₆)alkyl, aryl(Ci-C₆)alkanoyl, and heteroaryl (Ci- C₆)alkanoyl; wherein each (Ci-C₆)alkyl, (C₂-C6)alkenyl, (C₂-C6)alkynyl, (C]-C6)alkoxy, (C₃- C₆)cycloalkyI, and (C₁-C₆)alkanoyl of R³, R⁴, R⁵, and R⁶ is optionally substituted with one or more groups independently selected from halo, hydroxy, cyano, nitro, (CrC6)alkoxy, (C₃- C₆)cycloalkyl, oxo, carboxy, aryloxy, sulfo, -S(0)₂NR^5gR^5h, -N(R^5j)S(0)₂R^5k, -N⁺(R^5a)₃ D\

-C(=NR^5b)-NR^5cR^5d, or -NR^5e-C(= R^5b)-NR^5cR^5d and - R^5gR^5h; and wherein each aryl and heteroaryl of R³, R⁴, R⁵, and R⁶ is optionally substituted with one or more groups independently selected from (Ci-C6)alkyl, halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, (C₃-C₆)cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^5gR^5h, -N(R^Sj)S(0)₂R^5k, R^5s, -N⁺(R^5a)₃ D\ -C(=NR^5b)- NR^5cR^5d, or -NR^5e-C(=NR^Sb)-NR^5cR^5d, -NR^5gR^5h, and (C,-C₆)alkyl substituted with one or more groups independently selected from -N⁺(R^5a)₃ D-, -C(=NR^5b)-NR^5cR^5d, or -NR^5e-C(=NR^5b)- NR^5cR^5d, and -NR^5gR^5h;

each R^5a is independently selected from H, (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(C]-C₆) alkyl and heteroaryl(Ci-C6)alkyl;

each R^5b is independently selected from H, (Ci-Ce)alkyl, (C₃-C₆)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(Ci-C6) alkyl and heteroaryl(Ci-C6)alkyl;

each R^5c and R^5d is independently selected from H, (Ci-C6)alkyl, (C3-Ce)cycloalkyl, (C3- C6)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(C C6) alkyl and heteroaryl(Ci-C6) alkyl; or R^5c and R^5d together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; wherein any (Ci-C₆)alkyl, (C₃-C6)cycloalkyl, (C₃-C₆)cycloalkyl(C,-C₆)alkyl, aryl, heteroaryl, aryl(C,-C₆) alkyl or heteroaryl(C C₆)alkyl of R^5c and R^Sd is optionally substituted with one or more groups independently selected from hydroxy, carboxy, and NR^5mR^Sn;

each R^5e is independently selected from H, (Ci-Ce)alkyl, (C₃-Ce)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(C)-C₆) alkyl and heteroaryl(C C₆)alkyl;

each R^5f is independently selected from -N⁺(R^5a)₃ D^", -C(=NR^5b)-NR^5cR^5d, -NR^5e- C(=NR^5b)-NR^5cR^5d, -NR^5ce-C(=NR^5cb)R^5ce, -NR^5ce-C(=0)-NR^5ccR^5cd, and -NR^5gR^5h;

each R^5g and R^5h is independently selected from H, (Ci-C₆)alkyl, (C₃-C6)cycloalkyl, (C₃- C6)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(C]-C6) alkyl and heteroaryl(Ci-C₆) alkyl; or R^5g and R^5h together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; wherein any (C]-C6)alkyl, (C₃-C₆)cycloalkyl, (C₃-C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(C C₆) alkyl or heteroaryl(Ci-C₆)alkyl of R^Sg and R^5h is optionally substituted with one or more groups independently selected from hydroxy, carboxy, and NR^5mR⁵ⁿ;

each R^5j is independently selected from H, (Ci-C6)alkyl, (C₃-C6)cycloalkyl, (C₃- C6)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(Ci-C6) alkyl and heteroaryl (Ci-C6)alkyl;

each R^5k is independently selected from (CpCeJalkyl, (C₃-C6)cycloalkyl, (C₃- C6)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl(Ci-C₆)alkyl;

each R^5m and R⁵ⁿ is independently selected from H, (C,-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(C,-C₆) alkyl and heteroaryl(d-C₆) alkyl; or R^5m and R⁵ⁿ together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino;

each R^5s is independently trifluoromethyl, trifluoromethoxy, aryl, or heteroaryl, wherein each aryl and heteroaryl is optionally substituted with one or more (Ci-C6)alkyl, halo, hydroxy, cyano, nitro, (C₁-Ce)alkoxy, (C₃-C₆)cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^5gR^5h, -NR^5e- C(=NR^5b)-NR^5cR^5d and -NR^5gR^5h;

each R^5u and R^5v is independently selected from H and (Cj-C6)alkyl;

each R^5x is independently selected from (Ci-C6)alkyl, (Ci-C₆)alkanoyl, and

-C(=0)NR^5uR^5v;

each R^5y is independently selected from H and (Ci-Ce)alkyl;

each D^" is independently a counter anion;

each R^5cb is independently selected from H, (C^Ceialkyl, (C₃-C6)cycloalkyl, (C₃- C6)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(Ci-Ce) alkyl and heteroaryl(C]-C6)alkyl;

each R^5cc and R^5cd is independently selected from H, (Ci-C6)alkyl, (C₃-C6)cycloalkyl, (C₃-C6)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl(Ci-C₆) alkyl; or R^5cc and R^5cd together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; wherein any (Ci-Ce)alkyl, (C₃-C6)cycloalkyl, (C3-C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(C C₆) alkyl or heteroaryl(Ci-C₆)alkyl of R^5cc and R^5cd is optionally substituted with one or more groups independently selected from hydroxy, carboxy, and NR^5cmR^5cn;

each R^5ce is independently selected from H, (C_rC₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C6)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl(Ci-C₆)alkyl;

each R^5cm and R^5cn is independently selected from H, (C_rC₆)alkyl, (C₃-C₆)cycloalkyl, (C₃-C₆)cycloalkyl(CrC₆)alkyl, aryl, heteroaryl, aryl(C_rC₆) alkyl and heteroaryl(d-C₆) alkyl; or R^5cm and R^5cn together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino;

each R^5da is carboxy or (C] -C6)alkoxycarbonyl; and

the bond represented by— is present;

c) wherein:

X is ⁺N(R⁸¹)(R⁸²) B-;

Y is C(R⁸³);

R³ is:

A is N or C-R^4';

any adjacent R⁶, R⁷, R⁸, R⁴ and R⁵ taken together can optionally be methylenedioxy and each remaining R⁶, R⁷, R⁸, R⁴ and R⁵ is independently selected from H, fluoro, R^8bb, and Z-R^8x; each Z is independently selected from -0-, -S-, and -N(R^8y)-;

at least one of R⁴, R⁵, R² , R³ , and R⁶ is selected from hydroxy, carboxy, cyano, CF₃S0₃-, (C_rC₆)alkyl, (C₂-C₆)alkenyl, (C₂-C₆)alkynyl, (C C₆)alkoxy, cycloalkyl, aryl(C C₆)alkyl, aryl, heteroaryl, heteroaryl(C]-C₆)alkyl, arylalkanoyl, and heteroarylalkanoyl; and the remainder of R⁴, R⁵, R² , R³ , and R⁶ are independently selected from hydrogen, halo, hydroxy, carboxy, cyano, CF₃S0₃-, (Ci-C₆)alkyl, (C₂-C₆)alkenyl, (C₂-C₆)alkynyl, (Ci-Ce)alkoxy, cycloalkyl, aryl(Ci-C₆)alkyl, aryl, heteroaryl, heteroaryl(Ci-C₆)alkyl, aryl(Ci-C6)alkanoyl, and heteroaryl(C_rC₆)alkanoyl; or R^6' and R⁸¹ taken together are -(CR¹³₂)₂- or -CR¹⁴=CR¹⁴-;

wherein each (Ci-C6)alkyl, (C₂-C6)alkenyl, (C₂-C₆)alkynyl, (Ci-C6)alkoxy, cycloalkyl, and (Q- C₆)alkanoyl of R⁴, R⁵, R , R³ , and R⁶ is optionally substituted with one or more groups independently selected from halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, cycloalkyl, oxo, carboxy, aryloxy, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; and wherein each aryl, and heteroaryl of R⁴, R⁵, R² , R³ , and R⁶ is optionally substituted with one or more groups independently selected from (C]-C6)alkyl, halo, hydroxy, cyano, nitro, (Ci-C6)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, R^8aa, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h;

the bond represented by— is present and R⁸² is absent except as defined below when R⁸¹ and R^8a taken together with the atoms to which they are attached form a 5- or 6-membered heterocyclic ring or a 5- or 6-membered heteroaryl ring;

R⁸¹ is absent and B^* is absent; or R⁸¹ is H or (Ci-C₆)alkyl and B^" is counterion;

or R⁸¹ and R^8a taken together with the atoms to which they are attached form a 5- or 6- membered heterocyclic ring or a 5- or 6-membered heteroaryl ring, wherein a) when the bond represented by— is present in the 5- or 6-membered heterocyclic ring or the 5- or 6-membered heteroaryl ring, R⁸² is absent and B^" is a counterion, b) when the bond represented by— is

82 absent in the 5- or 6-membered heterocyclic ring or the 5- or 6-membered heteroaryl ring, R is (Ci-C6)alkyl and B^" is a counterion, or c) when the bond represented by— is absent in the 5- or 6-membered heterocyclic ring or the 5- or 6-membered heteroaryl ring, R is absent and B^" is absent;

R⁸³ is H, (C,-C₆)alkyl, (C,-C₆)alkoxy, (d-C₆)alkylthio, aryloxy, arylthio, -NR^8aR^8b, R^8cc, or cyano; or R^6' and R⁸³ taken together are -(CR¹³₂)₂- or -CR¹⁴=CR¹⁴-;

each R¹³ is independently H, (C)-C₆)alkyl, (C] -C₆)alkoxy, (d-C6)alkylthio, aryloxy or arylthio wherein any (Ci-Cg)alkyl, (Ci-C₆)alkoxy, and (C]-C6)alkylthio of R¹³ is optionally substituted with one or more groups selected from halo, cyano, oxo (=0), (Ci-C₆)alkyl, (C₃- Ce)cycloalkyl, carboxy, N0₂, hydroxy, (Ci-Ce)alkoxy, (C]-C6)alkoxycarbonyl, (Cp

C₆)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, and -NR^8eR^8f, and wherein any aryloxy, or arylthio of R¹³ is optionally substituted with one or more groups selected from halo, cyano, (Ci-Ce)alkyl, (C3-C6)cycloalkyl, carboxy, N0₂, hydroxy, (Ci-C6)alkoxy, (Ci-C6)alkoxycarbonyl, (C]-C6)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, and -NR^8eR^8f;

each R¹⁴ is independently H, (Ci-C6)alkyl, (Ci-C₆)alkoxy, (C]-C6)alkylthio, aryloxy or arylthio wherein any (Ci-Ce)alkyl, (Ci-Ce)alkoxy, and (Ci-C6)alkylthio of R¹⁴ is optionally substituted with one or more groups selected from halo, cyano, oxo (=0), (Ci-Ce)alkyl, (C₃- C₆)cycloalkyl, carboxy, N0₂, hydroxy, (CrC₆)alkoxy, (Ci-C₆)alkoxycarbonyl, (C\- Ce)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, and -NR^8eR^8f, and wherein any aryloxy, or arylthio of R¹⁴ is optionally substituted with one or more groups selected from halo, cyano, (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, carboxy, N0₂, hydroxy, (Ci-C₆)alkoxy, (Ci-C6)alkoxycarbonyl, (C]-C6)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, and -NR^8eR^8f;

R^8a is hydrogen, (Ci-Ce)alkyl, aryl, aryl(Ci-C₆)alkyl, heteroaryl, or heteroaryl (Ci- C6)alkyl; wherein each (C_rC6)alkyl of R ^a is optionally substituted with one or more groups selected from halo, hydroxy, cyano, nitro, (C]-C₆)alkoxy, cycloalkyl, oxo, carboxy,

and aryloxy, and wherein each aryl and heteroaryl of R^8a is optionally substituted with one or more groups selected from (Ci-C₆)alkyl, halo, hydroxy, cyano, nitro, (C]-C₆)alkoxy, cycloalkyl, carboxy, -NR^8gR^8h, and aryloxy;

R^8b is hydrogen, (Ci-C₆)alkyl, aryl, aryl(C]-C₆)alkyl, heteroaryl, heteroaryl(C C₆)alkyl, -C(=0)-R^8m, -C(=0)-OR⁸ⁿ, -C(=0)-SR^8p, -C(=0)-NR^8qR^8r, -C(=S)-R^8m, -C(=S)-OR⁸ⁿ,

-C(=S)-SR^8p, -C(=S)-NR^8qR^8r, or -C(=NR^8c)-R^8d; wherein each (C C₆)alkyl of R^8b is optionally substituted with one or more groups independently selected from halo, hydroxy, cyano, nitro, (C]-C6)aIkoxy, cycloalkyl, oxo, carboxy, and aryloxy; and wherein each aryl, and heteroaryl of R^8b is optionally substituted with one or more groups independently selected from (Cj-C6)alkyl, halo, hydroxy, cyano, nitro, (Ci-C6)alkoxy, cycloalkyl, carboxy, and aryloxy; or R^8a and R^8b taken together with the nitrogen to which they are attached form aziridino, azetidino, morpholino, piperazino, pyrrolidino, pyrrole, indole, or piperidino, which aziridino, azetidino, morpholino, piperazino, pyrrolidino pyrrole, indole, or piperidino can optionally be substituted with one or more (Ci-C6)alkyl;

R^8c is hydrogen, (Ci-C6)alkyl, aryl, or heteroaryl;

R^8d is hydrogen, (d-C₆)alkyl, (C_rC₆)alkoxy, (Ci-C₆)alkylthio, (C,-C₆)alkanoyl, or -NR^8eR^8f;

R^8e and R^8f are each independently selected from H, (Ci-Ce)alkyl, cycloalkyl, cycloalkyl(CrC6)alkyl, aryl, heteroaryl, aryl(Ci-C₆)alkyl and heteroaryl(Ci-C6)alkyl; or R^8e and R^8f together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino;

each R^8g and R^8h is independently selected from H, (Ci-Ce)alkyl, cycloalkyl,

cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(Ci-C₆)alkyl and heteroaryl(Ci-C6)alkyl; or R^gand R^h together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino;

each R^8j is independently selected from H, (Ci-C₆)alkyl, cycloalkyl, cycIoaIkyI(C]- Ce)alkyl, aryl, heteroaryl, aryl(Ci-C6)alkyl and heteroaryl(C_rC6)alkyl;

each R^8k is independently selected from (C]-C6)alkyl, cycloalkyl, cycloalkyl (Ci-C6)alkyl, aryl, heteroaryl, aryl(Ci-C6)alkyl and heteroaryl(Ci-C₆)alkyl;

each R^8m is independently selected from H, (C)-C₆)alkyl, cycloalkyl, cycloalkyl(C]- C6)alkyl, aryl, heteroaryl, aryl(Ci-C6)alkyl and heteroaryl(Ci-C6)alkyl;

each R⁸ⁿ is independently selected from H, (Ci-Ce)alkyl, cycloalkyl, cycloalkyl(Cr C₆)alkyl, aryl, heteroaryl, aryl(Ci-C6)alkyl and heteroaryl(C]-C6)alkyl, wherein each aryl, and heteroaryl is optionally substituted with one or more groups independently selected from (Ci- C6)alkyl, halo, hydroxy, cyano, nitro, (C)-C6)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h;

each R^8p is independently selected from H, (Ci-C₆)alkyl, cycloalkyl, cycloalkyl (Ci- Ce)alkyl, aryl, heteroaryl, aryl(Ci-C₆)alkyl and heteroaryl(C₁-C6)alkyl, wherein each aryl, and heteroaryl is optionally substituted with one or more groups independently selected from (C_r C₆)alkyl, halo, hydroxy, cyano, nitro, (Ci-Ce)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h;

each R^8q is independently selected from H, (Ci-C₆)alkyl, cycloalkyl, cycloalkyl (C\- Ce)alkyl, aryl, heteroaryl, aryl(Ci-C6)alkyl and heteroaryl(Ci-C6)alkyl; and each R^8r is independently selected from H, (Ci-C6)alkyl, cycloalkyl, cycloalkyl(C]-C6)alkyl, aryl, heteroaryl, aryl(Ci-C6)alkyl and heteroaryl(C]-C6)alkyl; or R^8q and R^8r together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; each R^8u and R^8v is independently selected from H and (Ci-Ce)alkyl;

each R^8x is independently selected from (Ci-C6)alkyl, (Ci-Ce)alkanoyl, and

-C(=0)NR^8uR^8v;

each R^8y is independently selected from H and (Ci-C6)alkyl;

each R^8aa is independently selected from aryl and heteroaryl, which aryl and heteroaryl is optionally substituted with one or more groups independently selected from (Ci-C₆)alkyl, halo, hydroxy, cyano, nitro, (C_rC6)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8gR^8h, -N(R^j)S(0)₂R^8k, and -NR^8gR^8h;

each R^8bb is independently selected from aryl and heteroaryl, which aryl and heteroaryl is optionally substituted with one or more groups independently selected from (C]-C₆)alkyl, halo, hydroxy, cyano, nitro, (Ci-Ce)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h;

R^8cc is (Ci-C₆)alkyl which is substituted with one or more -N⁺(R^8ha)₃ B\ -C(=NR^8hb)- NR^8hcR^8hd, -NR ^he-C(=NR^8hb)-NR^8hcR^8hd, -NR^8ke-C(=NR^8kb)R^8ke, or -NR^8ke-C(=0)-NR^8kcR^8kd; each R^8ha is independently selected from H, (Ci-Ce)alkyl, (C₃-C6)cycloalkyl, (C₃- C6)cycloalkyl(C₁-C6)alkyl, aryl, heteroaryl, aryl(Ci-C6) alkyl and heteroaryl(Ci-C6)alkyl;

each R is independently selected from H, (Ci-C6)alkyl, (C₃-C6)cycloalkyl, (C₃- C6)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(Ci-C6) alkyl and heteroaryl(Ci-C6)alkyl;

each R^8hc and R^8hd is independently selected from H, (C C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃-C6)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(Ci-C6) alkyl and heteroaryl (Ci-C₆) alkyl; or R and R together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; wherein any (C]-C6)alkyl, (C₃-C₆)cycloalkyl, (C₃-C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(C_rC₆) alkyl or heteroaryl(Ci-C₆)alk I of R^hc and R^hd is optionally substituted with one or more groups independently selected from hydroxy, carboxy, and NR^8hmR^8hn;

each R^8he is independently selected from H, (Ci-C₆)alkyl, (C₃-C₆)cycloaIkyl, (C₃- C6)cycloalkyl(C C₆)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl(Ci-C₆)alkyl;

each R^8hm and R^8hn is independently selected from H, (C C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃-C6)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl (Ci-C₆) alkyl; or R^8hm andR^8hn together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino;

each R^8kb is independently selected from H, (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C₆)cycIoalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(C]-C₆) alkyl and heteroaryl(Ci-C₆)alkyl;

each R^8kc and R^kd is independently selected from H, (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C₆)cycloalkyl(C₁-C₆)alkyl, aryl, heteroaryl, aryl(C_rC₆) alkyl and heteroaryl(Ci-C₆) alkyl; or R^8kc and R^8kd together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; wherein any (Ci-C6)alkyl, (C₃-C6)cycloalkyl, (C₃-C6)cycloalkyl(Ci-Ce)alkyl, aryl, heteroaryl, aryl(Ci-C6) alkyl or heteroaryl(Ci-C6)alkyl of R^8kc and R^8kd is optionally substituted with one or more groups independently selected from hydroxy, carboxy, and NR^8kmR^8kn;

each R^8ke is independently selected from H, (Ci-C6)alkyl, (C₃-C6)cycloalkyl, (C₃- C6)cycloalkyl(C₁-C₆)alkyl, aryl, heteroaryl, aryl(Ci-Ce) alkyl and heteroaryl(Ci-C6)alkyl; and each R^8km and R^8kn is independently selected from H, (C_f-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃-C6)cycloalkyl(C₁-C6)alkyl, aryl, heteroaryl, aryl(Ci-C6) alkyl and heteroaryl(C]-C6) alkyl; or R^8km and R^8kn together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; and

each B^" is a counterion;

or a salt or prodrug thereof.

2. The compound of claim 1 wherein:

R¹ is R^y or (C)-C6)alkyl that is substituted with one or more R^y;

R² is R^z or (C] -C6)alkyl that is substituted with one or more R ;

at least one of R⁴ R⁵ R⁶ and R⁷ is aryl or heteroaryl wherein each aryl or heteroaryl is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^d; and the remainder of R⁴ R⁵ R⁶ and R⁷ are each independently H, halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl,

trifluoromethoxy, (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, (C]-C₆)alkoxy, (Q-Ceialkoxycarbonyl, (C C6)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, (Ci-C6)alkylthio, -S(0)R^P, -S(0)₂R^P, -S(0)₃R^P, -S(0)₂NR^ER^H, and -NR^GR^H; wherein any alkyl and any alkyl or alkanoyl portion of any aryl(C₁-C₆)alkyl, heteroaryl(Ci-C₆)alkyl, aryl(Ci-C6)alkanoyl or heteroaryl(Ci-C₆)alkanoyl is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^A ; and wherein any aryl, heteroaryl, or any aryl or heteroaryl portion of any aryl(Ci-C₆)alkyl, heteroaryl(Ci-C₆)alkyl, aryl(Cr

C₆)alkanoyl or heteroaryl(Ci-C6)alkanoyl of R⁴ R⁵ R⁶ and R⁷ is optionally substituted with one or more (e.g. 1 , 2, 3, or 4) R^B;

R⁸ is H, halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (Q- C₆)alkyl, (C₃-C6)cycloalkyl, (Ci-C6)alkoxy, (C]-C₆)alkoxycarbonyl, (Ci-C6)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, (C,-C₆)alkylthio, -S(0)R^P, -S(0)₂R^P, -S(0)₃R^P, -S(0)₂NR^GR^H, and -NR^GR^H; wherein any alkyl of R⁸ is optionally substituted with one or more (e.g. 1 , 2, 3, or 4) R^A ; and wherein any aryl, or heteroaryl of R⁸ is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^B;

X is N; Y is C(R²); and R³ is R^E; or

X is N; Y is C(R¹⁵); and R³ is R^C; or

X is C(R'); Y is N; and R³ is R^C or

X is C(R¹⁶); Y is C(R^N); and R³ is R^E ; or

X is C(R'); Y is C(R¹²); and R³ is R^E ; or

X is N⁺- R¹³ (ZO; Y is C(R¹²); and R³ is R^C ; or

X is C(R¹⁰); Y is N⁺-R¹⁴ (Z^"); and R³ is R^C;

each R¹⁰ is H, halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (Ci-C6)alkyl, (C₃-C6)cycloalkyl, (Ci-Ce)alkoxy, (C₁-C₆)alkoxycarbonyl, (Ci-C₆)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, and -NR^GR^H; wherein any alkyl of R¹⁰ is optionally substituted with one or more (e.g. 1 , 2, 3, or 4) R^A ; and wherein any aryl, heteroaryl, or any aryl or heteroaryl portion of any aryl(Ci-C6)alkyl, heteroaryl(Ci-C6)alkyl, aryloxy, or heteroaryloxy of R¹⁰ is optionally substituted with one or more (e.g. 1 , 2, 3, or 4) R^B;

each R^U is H, halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (Ci-C6)alkyl, (C₃-C6)cycloalkyl, (d-C₆)alkoxy, (C]-C6)alkoxycarbonyl, (Ci-C6)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, and -NR^GR^H; wherein any alkyl and any alkyl or alkanoyl portion of any aryl(Ci-C6)alkyl, heteroaryl(Ci-C₆)alkyl, aryl(Ci-C6)alkanoyl or heteroaryl(Ci-C6)alkanoyl of R^N is optionally substituted with one or more (e.g. 1 , 2, 3, or 4) R^A ; and wherein any aryl, heteroaryl, or any aryl or heteroaryl portion of any aryl(Ci-C6)alkyl, heteroaryl(Ci-C6)alky], aryl(Ci-C₆)alkanoyl or heteroaryl(Ci-C₆)alkanoyl of Rⁿ is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^b;

each R¹² is H, halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (C_rC₆)alkyl, (C₃-C₆)cycloalkyl, (C C₆)alkoxy, (C C₆)alkoxycarbonyl, (Ci-C₆)alkanoyloxy, aryloxy, heteroaryloxy, and -NR^eR^h; wherein any alkyl and any alkyl or alkanoyl portion of any aryl(Ci-C₆)alkyl, heteroaryI(C_rC₆)alkyl, aryl(d-C₆)alkanoyl or heteroaryl(Ci-C₆)alkanoyl of R¹² is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^a ; and wherein any aryl, heteroaryl, or any aryl or heteroaryl portion of any aryl(Ci-C6)alkyl, heteroaryl (Ci-C6)alkyl, aryl(Ci-C6)alkanoyl or heteroaryl(C)-C₆)alkanoyl of R¹² is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^b;

each R¹³ is (C C₆)alkyl, aryl, or aryl(C C₆)alkyl;

each R¹⁴ is (Q-Q alkyl, aryl, or aryl(d-C₆)alkyl;

R¹⁵ is R^x or (C C6)alkyl that is substituted with one or more R^x;

R¹⁶ is R^z or (Ci-C6)alkyl that is substituted with one or more R^y;

each R^a is independently selected from halo, cyano, nitro, hydroxy, carboxy, oxo, (Q- C₆)alkyl, (C₃-C6)cycloalkyl, (C]-C₆)alkoxy, (Ci-C₆)alkoxycarbonyl, (C]-C6)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, (C)-C₆)alkylthio, -S(0)R^p, -S(0)₂R^p, -S(0)₃R^p, -S(0)₂NR^gR^h, and -NR^gR^h; wherein each aryl, heteroaryl, aryloxy, and heteroaryloxy is optionally substituted with one or more (e.g. 1, 2, 3, or 4) groups independently selected from halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (Ci-Ce)alkyl, (C₃-C6)cycIoalkyl, (Q- C₆)alkoxy, (C C₆)alkoxycarbonyl, (d-C₆)alkanoyloxy, (C C₆)alkylthio, -S(0)R^p, -S(0)₂R^p, -S(0)₃R^p -S(0)₂NR^gR^h, and -NR^gR^h;

each R^b is independently selected from halo, cyano, nitro, hydroxy, carboxy,

trifluoromethyl, trifluoromethoxy, (Ci-Ce)alkyl, (C₃-C6)cycloalkyl, (C₁-C6)alkoxy, (Ci- C6)alkoxycarbonyl, (Ci-C6)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, (Ci- C₆)alkylthio, -S(0)R^p, -S(0)₂R^p, -S(0)₃R^p, -S(0)₂NR^gR^h, and -NR^gR^h; wherein each aryl, heteroaryl, aryloxy, and heteroaryloxy is optionally substituted with one or more (e.g. 1, 2, 3, or 4) groups independently selected from halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (Ci-C₆)alky], (C₃-C6)cycloalkyl, (Ci-C6)alkoxy, (C]-C₆)alkoxycarbonyl, (C_r C₆)alkanoyloxy, (Ci-C₆)alkylthio, -S(0)R^p, -S(0)₂R^p, -S(0)₃R^p, -S(0)₂NR^gR^h, and -NR^gR^h; each R^c is H, halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, (C C6)alkoxy, (Ci-C6)alkoxycarbonyl, (Ci-Ce)alkanoyloxy, aryl other than phenyl, heteroaryl other than pyrid-4-yl, aryloxy, heteroaryloxy, and -NR^gR^h; wherein any alkyl and any alkyl or alkanoyl portion of any aryl(Ci-C6)alkyl, heteroaryl(Ci-C6)alkyl, aryl(Ci-C6)alkanoyl or heteroaryl(C_rC6)alkanoyl of R° is optionally substituted with one or more (e.g. 1 , 2, 3, or 4) R^a ; and wherein any aryl, heteroaryl, or any aryl or heteroaryl portion of any aryl(CrC₆)alkyl, heteroaryl (d-C₆)alkyl, aryl(Ci-C₆)alkanoyl or heteroaryl(Ci-C₆)alkanoyl of R^c is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^b;

each R^d is independently selected from halo, cyano, nitro, hydroxy, carboxy,

trifluoromethyl, trifluoromethoxy, (Ci-C₆)alkyl, (C₃-C6)cycloalkyI, (Q-C₆)alkoxy, (Q- C₆)alkoxycarbonyl, (Ci-C₆)aIkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, and -NR^gR^h; wherein each aryl, heteroaryl, aryloxy, and heteroaryloxy is optionally substituted with one or more (e.g. 1, 2, 3, or 4) groups independently selected from halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (C_rC₆)alkyl, (C₃-C₆)cycloalkyl, (C_rC₆)alkoxy, (Ci- C₆)alkoxycarbonyl, (Ci-Ce)alkanoyloxy, and -NR^gR^h;

each R^e is H, halo, cyano, nitro, hydroxy, carboxy, trifluoromethyl, trifluoromethoxy, (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, (C C6)alkoxy, (Ci-C₆)alkoxycarbonyl, (Ci-C₆)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, and -NR^gR^h; wherein any alkyl and any alkyl or alkanoyl portion of any aryl(C₁-C₆)alkyl, heteroaryl(Ci-C₆)alkyl, aryl(Ci-Ce)alkanoyl or heteroaryl(Ci-C₆)alkanoyl of R^e is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^a ; and wherein any aryl, heteroaryl, or any aryl or heteroaryl portion of any aryl(Ci-C6)alkyl, heteroaryl(Ci-C₆)alkyl, aryl(Ci-C₆)alkanoyl or heteroaryl(Ci-C₆)alkanoyl of R^e is optionally substituted with one or more (e.g. 1, 2, 3, or 4) R^b;

each R^g and R^h is independently selected from H, (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C6)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl(Ci-C₆) alkyl; or R^g and R^h together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidine or piperidino; wherein any (Ci-Ce)alkyl, (C3-C₆)cycloalkyl, (C₃-C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl or heteroaryl(Ci-C₆)alkyl of R^g and R^h is optionally substituted with one or more groups independently selected from hydroxy, carboxy, and NR'R^U;

each R^J is independently selected from H, (Ci-C6)alkyl, (C₃-C6)cycloalkyl, (C₃- C6)cycloalkyl(C₁-C6)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl(Ci-C₆)alkyl;

each R^m and Rⁿ is independently selected from H, (C C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(C C₆) alkyl and heteroaryI(d-C₆) alkyl; or R^m andR" together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; wherein any (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃-C6)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(C)-C6) alkyl or heteroaryl (C C₆) alkyl of R^m and Rⁿ is optionally substituted with one or more groups independently selected from hydroxy, carboxy, and NR^lR^u;

each R^p is independently selected from H, (Ci-C6)alkyl, (C₃-C6)cycloalkyl, (C₃- C6)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(C]-C6) alkyl and heteroaryl (Ci-C₆) alkyl; each R^q is independently selected from H, (C_rC6)alkyl, (C₃-C6)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(Ci-Ce) alkyl and heteroaryl(Ci-C₆)alkyl; each R^s is independently selected from H, (Ci-Ce)alkyl, (C₃-C6)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl(C]-C₆)alkyl; each R^l and R^u is independently selected from H, (Ci-Cejalkyl, (C₃-C6)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(C]-C6) alkyl and heteroaryl(Ci-C6) alkyl; or R'and R^u together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino;

each R^x is independently -NR^mRⁿ, -N⁺ (R^s)₃ Z\ -C(=NR^j)-NR^mRⁿ, or -NR^q-C(=NR^j)- NR^mRⁿ;

each R^y is independently -NR^mRⁿ, -N^4" (R^s)₃ Z\ -C(=NR^j)-NR^mRⁿ, or -NR^q-C(=NR^j)- NR^mRⁿ;

each R^z is independently -C(=NR^j)-NR^mRⁿ, or -NR^q-C(=NR^J)-NR^mRⁿ;

the bond represented by— is present; and

each Z^" is independently an acceptable counterion;

or a salt or prodrug thereof.

3. The compound o claim 1 which is a compound of formula (la) or (lb):

(la) (lb)

or a salt or prodrug thereof.

4. The compound of claim 1 which is a com ound of formula (Ic):

(Ic) or a salt or prodrug thereof.

The compound of claim 1 which is a compound of formula (Id) or

(le) or a salt or prodrug thereof.

The compound of claim 1 which is a compound of formula (If)

or a salt or prodrug thereof.

8. T compound of claim 1 which is a compound of formula:

or a salt or prodrug thereof.

9. compound of claim 1 which is a compound of formula:

or a salt or prodrug thereof.

The com ound of claim 1 which is a compound of formula:

or a salt or prodrug thereof.

1 1. The compound of any one of claims 1-6 wherein R⁴ is phenyl, biphenyl, cyclopropyl, tert-buty phenyl, or furyl.

12. The compound of any one of claims 1-6 wherein R⁵ is phenyl, biphenyl, cyclopropyl, tert-butylphenyl, or furyl.

13. The compound of any one of claims 1-6 wherein R⁶ is phenyl, biphenyl, cyclopropyl, tert-butylphenyl, or furyl.

14. The compound of any one of claims 1-6 wherein R⁷ is phenyl, biphenyl, cyclopropyl, tert-butylphenyl, or furyl.

15. The compound of claim 1, 2, 3, or 7 wherein R^x is -NR^mRⁿ.

16. The compound of claim 1, 2, 3, or 6 wherein R^x is -N⁺ (R^s)₃ Z^".

17. The compound of claim 1, 2, 3, or 6 wherein R is -C(=NR^j)-NR^mRⁿ.

18. The compound of claim 1 , 2, 3, or 6 wherein R^x is -NR^q-C(=NR^j)-NR^mRⁿ.

19. The compound of claim 1, 2, 4, 5, 8, or 9 wherein R^y is -NR^mR".

20. The compound of claim 1, 2, 4, 5, 8, or 9 wherein R^y is -N ^" (R^s)₃ Z^".

21. The compound of claim 1, 2, 4, 5, 8, or 9 wherein R^y is -C(=NR^J)-NR^mRⁿ.

22. The compound of claim 1, 2, 4, 5, 8, or 9 wherein R^y is -NR^q-C(=NR^J)-NR^mRⁿ.

23. The compound of claim 1 , 2, 5, or 9 R^z is -C(=NR^j)-NR^mRⁿ.

24. The compound of claim 1 , 2, 5, or 9 wherein R^z is -NR^q-C(=NR^J)-NR^mR".

25. The compound of claim 1 which is:

or a salt or prodrug thereof.

26. The compound of claim 1 which is:

or a salt or prodrug thereof.

27. The compound of claim 1 wherein:

X is W-R⁵¹;

Y is C(R⁵²);

W is N; R⁵¹ is absent; or

W is N⁺D^"; R⁵¹ is (d-C₆)alkyl, aryl, or ai l(Ci-C₆)alkyl; or

W is C; R⁵¹ is hydrogen, -N⁺(R^5a)₃ D\ -C(=NR^5b)-NR^5cR^5d, -NR^e-C(=NR^5b)-NR^5cR^5d, -NR^5gR^5h, -NR^5ce-C(=NR^5cb)R^5ce, -NR^5ce-C(=0)-NR^5ccR^5cd, or (C,-C₆)alkyl that is substituted with one or more R ;

R⁵² is a ring selected from :

wherein:

any adjacent R⁶, R⁷, R⁴ and R⁵ taken together can optionally be methylenedioxy and each remaining R⁶, R⁷, R⁴ and R^s is independently selected from H, Z-R^x, R^f, and (Ci-C₆)alkyl that is substituted with one or more R^f;

the bond represented by— is present;

R⁷ is absent and B~ is absent; or R⁷ is (Ci-C6)alkyl and B^" is a counterion; and

R⁸ is absent and B^" is absent; or R⁸ is (Ci-C₆)alkyl and B^" is a counterion.

The compound of claim 27 which is a compound of formula Va:

(Va)

wherein:

X is N or C(R^56');

W is N; R⁵¹ is absent; or

W is N; R⁵¹ is (Ci-C₆)alkyl, aryl, or aryl(Ci-C6)alkyl; and A^" is counter anion; or

W is C; R⁵¹ is hydrogen, -N⁺(R^5a)₃ D\ -C(=NR^Sb)-NR^5cR^5d, -NR^5e-C(=NR^5b)-NR^5cR^5d,

-NR^5gR^5h, -NR^5ce-C(=NR^5cb)R^5ce, -NR^5ce-C(=0)-NR^5ccR^5cd, or (C,-C₆)alkyl that is substituted with one or more R^5f; and A^" is absent;

Y is N; R⁵² is absent; and B^" is absent; or

Y is N; R⁵² is (C] -C6)alkyl, aryl, or aryl(C] -C6)alkyl; and B^" is counter anion; or

Y is C; R^52' is hydrogen, -N⁺(R^5a)₃ D\ -C(=NR^5b)-NR^5cR^5d, -NR^e-C(=NR^5b)-NR^5cR^5d, -NR^5ce-C(=NR^5cb)R^5ce, -NR^5ce-C(=0)-NR^5ccR^5cd, -NR^5gR^5h, or (C C₆)alkyl that is substituted with one or more R^5f; and B^" is absent;

any adjacent R⁶, R⁷, R⁵³ , R⁵⁴ and R⁵⁵ taken together can optionally be methylenedioxy and each remaining R⁶, R⁷, R⁵³ , R^54' and R⁵⁵ is independently selected from H, Z-R^5x, R^5f, and (C]-C₆)alkyl that is substituted with one or more R^5f; or R⁵⁴ can be R^5da;

R⁸ is hydrogen, (Ci-C₆)alkyl, aryl, or aryl(Ci-Ce)alkyl wherein each (Ci-C6)alkyl of R⁸ is optionally substituted with one or more groups independently selected from halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, (C₃-C6)cycloalkyl, oxo, carboxy, aryloxy, sulfo, and -NR^5gR^5h, and wherein each aryl of R⁸ is optionally substituted with one or more groups independently selected from (Ci-C₆)alkyl, halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, (C₃-C6)cycloalkyl, carboxy, aryloxy, nitro, R^5s, and -NR^5gR^5h;

each Z is independently selected from -0-, -S-, and -N(R^5y)-;

at least one of R³, R⁴, R⁵, and R⁵⁶ is selected from hydroxy, carboxy, cyano, CF3SO3-, (C C₆)alkyl, (C₂-C₆)alkenyl, (C₂-C₆)alkynyl, (C C₆)alkoxy, (C₃-C₆)cycloalkyl, aryl(C_rC₆)alkyl, aryl, heteroaryl, heteroaryl(Ci-C6)alkyl, aryl(d-C6)alkanoyl, and heteroaryl(d-C6)aIkanoyl; and the remainder of R³, R⁴, R⁵, and R⁵⁶ are independently selected from H, hydroxy, carboxy, cyano, CF3SO3-, (C,-C₆)alkyl, (C₂-C₆)alkenyl, (C₂-C₆)alkynyl, (C₁-C₆)alkoxy, (C₃-C₆)cycloalkyl, aryl(C]-C6)alkyl, aryl, heteroaryl, heteroaryl(d-C6)alkyl, aryl(Ci-C₆)alkanoyl, and heteroaryl(d- C₆)alkanoyI; wherein each (d-C₆)alkyl, (C₂-C₆)alkenyl, (C₂-C6)alkynyl, (d-Ce)alkoxy, (C₃- C₆)cycloalkyl, and (Ci-C6)alkanoyl of R³, R⁴, R⁵, and R⁵⁶ is optionally substituted with one or more groups independently selected from halo, hydroxy, cyano, nitro, (C]-C₆)alkoxy, (C₃- C₆)cycIoalkyl, oxo, carboxy, aryloxy, sulfo, -S(0)₂NR^5gR^sh, -N(R^5j)S(0)₂R^5k, -N⁺(R^5a)₃ D^", -C(=NR^5b)-NR^5cR^5d, or -NR^5e-C(=NR^5b)-NR^5cR^5d and -NR^5gR^5h; and wherein each aryl and heteroaryl of R³, R⁴, R⁵, and R⁵⁶ is optionally substituted with one or more groups independently selected from (d-C6)alkyl, halo, hydroxy, cyano, nitro, (d-C6)alkoxy, (C3-Ce)cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^SgR^5h, -N(R^5j)S(0)₂R^5k, Rv^s, -N⁺(R^5a)₃ D^", -C(=NR^5b)- NR^5cR^5d, or -NR^5e-C(=NR^5b)-NR^5cR^5d, -NR^5gvR^h, and (C,-C₆)alkyl substituted with one or more groups independently selected from -^(R⁵^ D^", -C(=NR^5b)-NR^ScR^5d, or -NR^5e-C(=NR^5b)- NR^ScR^5d, and -NR^5gR^5h;

each R^5a is independently selected from H, (C₁-C₆)alkyl, (C3-Ce)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(Q-C6) alkyl and heteroaryl(C]-C6)alkyl;

each R^5b is independently selected from H, (Ci-C6)alkyl, (C3-C₆)cycloalkyl, (C3- C6)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(Ci-Ce) alkyl and heteroaryl(Ci-C6)alkyl;

each R^5c and R^5d is independently selected from H, (C]-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C6)cycloalkyl(d-C6)alkyl, aryl, heteroaryl, aryl(d-C6) alkyl and heteroaryl(Ci-C6) alkyl; or R^5c andR^5d together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; wherein any (Ci-Ce)alkyl, (C3-C6)cycloalkyl, (C₃-C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(d-C₆) alkyl or heteroaryl(C_rC₆)aIkyI of R^c and R^5d is optionally substituted with one or more groups independently selected from hydroxy, carboxy, and NRv^mR⁵ⁿ;

each R^5e is independently selected from H, (C]-C6)alkyl, (C3-C6)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(C)-C₆) alkyl and heteroaryl(Ci-C₆)alkyl;

each R^5f is independently selected from -N⁺(R^5a)₃ D^", -C(=NR^5b)-NR^5cR^5d, -NR^5e- C(=NR^5b)-NR^5cR^5d, -NR^5ce-C(=NR^5cb)R^5ce, -NR^5ce-C(=0)-NR^5ccR^5cd, and -NR^5gR^5h; each R^5g and R^5h is independently selected from H, (C]-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl(C_rC₆) alkyl; or R^5g and R^5h together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; wherein any (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃-C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(C,-C₆) alkyl or heteroaryl(C,-C₆)alkyl of R^5g and R^5h is optionally substituted with one or more groups independently selected from hydroxy, carboxy, and NR^5mR⁵ⁿ;

each R⁵' is independently selected from H, (Ci-Ce)alkyl, (C₃-C₆)cycloalkyl, (C₃- C₆)cycloalkyl(C]-C₆)alkyl, aryl, heteroaryl, aryl(Ci-Ce) alkyl and heteroaryl(Ci-Ce)alkyl;

each R^5k is independently selected from (Ci-C₆)alkyl, (C₃-Ce)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl(Ci-C₆)alkyl;

each R^5m and R⁵ⁿ is independently selected from H, (d-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C₆)cycloalkyl(CrC₆)alkyl, aryl, heteroaryl, aryl(d-C₆) alkyl and heteroaryl(C_rC₆) alkyl; or R^Sm and R⁵ⁿ together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino;

each R^5s is independently trifluoromethyl, trifiuoromethoxy, aryl, or heteroaryl, wherein each aryl and heteroaryl is optionally substituted with one or more (Ci-Ce)alkyl, halo, hydroxy, cyano, nitro, (C]-C₆)alkoxy, (C₃-C₆)cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^gR^h, -N(R^j)S(0)₂R^k, trifluoromethyl, trifiuoromethoxy, -N⁺(R^5a)₃ D^", -C(=NR^5b)-NR^5cR^5d, -NR^5e- C(=NR^5b)-NR^ScR^5d and -NR^5gR^5h;

each R^5u and R^5v is independently selected from H and (Ci-Ce)alkyl;

each R^5x is independently selected from (Cj-C₆)alkyl, (C]-C₆)alkanoyl, and

-C(=0)NR^SuR^Sv;

each R^5y is independently selected from H and (Ci-C₆)alkyl;

each D^" is independently a counter anion;

each R^5cb is independently selected from H, (C]-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C6)cycloalkyl(C]-C6)alkyl, aryl, heteroaryl, aryl(C]-C6) alkyl and heteroaryl(Ci-C₆)alkyl;

each R^Sc and R^5cd is independently selected from H, (Ci-Ce)alkyl, (C₃-Ce)cycloalkyl, (C₃-C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(C)-C₆) alkyl and heteroaryl (CrC₆) alkyl; or R^5cc and R^5cd together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; wherein any (C₁-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃-C6)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(Ci-Ce) alkyl or heteroaryl(Ci-C₆)alkyl of R^5cc and R^5cd is optionally substituted with one or more groups independently selected from hydroxy, carboxy, and NR^5cmR^5cn; each R is independently selected from H, (C_rC₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(C]-C₆) alkyl and heteroaryl(C]-C₆)alkyl; and each R^5cm and R^5cn is independently selected from H, (C]-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃-C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(CrC₆) alkyl and heteroaryl(C]-C₆) alkyl; or R^cm and R"¹ together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino;

each R^5da is carboxy or (C_rC₆)alkoxycarbonyl; and

or a salt or prodrug thereof.

29. The compound of claim 28 wherein:

X is N or C(R^56');

W is N; R⁵¹ is absent; and A^" is absent; or

W is N; R⁵¹ is (Ci-C₆)alkyl, aryl, or aryl(Ci-C₆)alkyl; and A^" is counter anion; or

W is C; R⁵¹ is hydrogen, -N⁺(R^Sa)₃ D^", -C(=NR^5b)-NR^5cR^5d, -NR^5e-C(=NR^5b)-NR^5cR^5d, -NR^5gR^5h, or (C]-C₆)alkyl that is substituted with one or more R^5f; and A^" is absent;

Y is N; R⁵² is absent; and B^" is absent; or

Y is N; R⁵² is (C]-C₆)alkyl, aryl, or aryl(Ci-C₆)alkyl; and B^" is counter anion; or

Y is C; R^52' is hydrogen, -N⁺(R^5a)₃ D^", -C(=NR^5b)-NR^5cR^5d, -NR^5e-C(=N⁵R^b)-NR^5cR^5d, -NR^5gR^5h, or (Ci-C₆)alkyl that is substituted with one or more R^5f; and B^" is absent;

any adjacent R⁶, R⁷, R⁵³ , R⁵⁴ and R⁵⁵ taken together can optionally be methylenedioxy and each remaining R⁶, R⁷, R⁵³ , R^54' and R⁵⁵ is independently selected from H, Z-R^5x, R^5f, and (Ci-C₆)alkyl that is substituted with one or more R^5f;

R⁸ is hydrogen, (Ci-C6)alkyl, aryl, or aryl(C]-C₆)alkyl wherein each (C]-C₆)alkyl of R⁸ is optionally substituted with one or more groups independently selected from halo, hydroxy, cyano, nitro, (CrC₆)alkoxy, (C₃-Ce)cycloalkyl, oxo, carboxy, aryloxy, sulfo, and -NR^5gR^5h, and wherein each aryl of R⁸ is optionally substituted with one or more groups independently selected from (Ci-C6)alkyl, halo, hydroxy, cyano, nitro, (Ci-C6)alkoxy, (C₃-C6)cycloalkyl, carboxy, aryloxy, nitro, R^5s, and -NR^5gR^5h;

each Z is independently selected from -0-, -S-, and -N(R^5y)-;

at least one of R³, R⁴, R⁵, and R⁵⁶ is selected from hydroxy, carboxy, cyano, CF₃S0₃-, (Ci-C₆)alkyl, (C₂-C₆)alkenyl, (C₂-C₆)alkynyl, (Ci-C₆)alkoxy, (C₃-C₆)cycloalkyl, aryl(Ci-C₆)alkyl, aryl, heteroaryl, heteroaryl(Ci-C₆)alkyl, aryl(Ci-C₆)alkanoyl, and heteroaryl(Ci-C₆)alkanoyl; and the remainder of R³, R⁴, R⁵, and R⁶ are independently selected from H, hydroxy, carboxy, cyano, CF₃S0₃-, (Ci-C₆)alkyl, (C₂-C₆)alkenyl, (C₂-C₆)alkynyl, (C C₆)alkoxy, (C₃-C₆)cycloalkyl, aryl(Ci-C₆)alkyl, aryl, heteroaryl, heteroaryl(Ci-C₆)alkyl, aryl(Ci-C₆)alkanoyl, and heteroaryl(Cp C₆)alkanoyl; wherein each (C]-C₆)alkyl, (C₂-C₆)alkenyl, (C₂-C₆)alkynyl, (C_rC₆)alkoxy, (C₃- C6)cycloalkyl, and (C C6)alkanoyl of R³, R⁴, R⁵, and R⁵⁶ is optionally substituted with one or more groups independently selected from halo, hydroxy, cyano, nitro, (C]-C₆)alkoxy, (C₃- C₆)cycloalkyl, oxo, carboxy, aryloxy, sulfo, -S(0)₂NR^5gR^5h, -N(R^5j)S(0)₂R^5k, -N⁺(R^5a)₃ D^', -C(=NR^5b)-NR^5cR^5d, or -NR^5e-C(=NR^5b)-NR^5cR^5d and -NR^5gR^5h; and wherein each aryl and heteroaryl of R³, R⁴, R⁵, and R⁵⁶ is optionally substituted with one or more groups independently selected from (Ci-C6)alkyl, halo, hydroxy, cyano, nitro, (Ci-Ce)alkoxy, (C₃-C₆)cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^5gR^5h, -N(R^5j)S(0)₂R^5k, R^5s, -N⁺(R^5a)₃ D^", -C(=NR^5b)- NR^5cR^5d, or -NR^5e-C(=NR^5b)-NR^5cR^sd, -NR^5g5R^h, and (C,-C₆)alkyl substituted with one or more groups independently selected from -N⁺(R^5a)₃ D\ -C(=NR^Sb)-NR^5cR^5d, or -NR^5e-C(=NR^5b)- NR^5cR^5d, and -NR^5gR^5h;

each R^5a is independently selected from H, (C C₆)alky], (C₃-C₆)cycloalkyl, (C₃- C6)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(Cj-C6) alkyl and heteroaryl(Ci-C6)alkyl;

each R^5b is independently selected from H, (Ci-C6)alkyl, (C₃-Ce)cycloalkyl, (C₃- C6)cycloalkyl(C]-C6)alkyl, aryl, heteroaryl, aryl(Ci-C6) alkyl and heteroaryl(C)-C6)alkyl;

each R^5c and R^5d is independently selected from H, (Ci-C6)alkyl, (C₃-Ce)cycloalkyl, (C₃- C₆)cycloalkyl(C]-C6)alkyl, aryl, heteroaryl, aryl(Ci-C6) alkyl and heteroaryl(C]-C6) alkyl; or R^5c and R^5d together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; wherein any (Ci-C6)alkyl, (C₃-C6)cycloalkyl, (C₃-C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(d-C₆) alkyl or heteroarylCQ-Ceialkyl of R^c and R^d is optionally substituted with one or more groups independently selected from hydroxy, carboxy, and NR^5mR⁵ⁿ;

each R^5e is independently selected from H, (Ci-Ce)alkyl, (C₃-C6)cycloalkyl, (C₃- C6)cycloalkyl(C]-C6)alkyl, aryl, heteroaryl, aryl(Ci-Ce) alkyl and heteroary](Ci-C₆)alkyl;

each R^5f is independently selected from -N⁺(R^5a)₃ D^", -C(=NR^5b)-NR^5cR^5d, -NR^5e- C(=NR^5b)-NR^5cR^5d, and -NR^5gR^5h;

each R^5g and ⁵R^h is independently selected from H, (Ci-C6)alkyl, (C₃-Ce)cycloalkyl, (C₃- C₆)cycloalkyl(C_rC₆)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl(C C₆) alkyl; or R^5g and R^5h together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; wherein any (C]-C6)alkyl, (C₃-C6)cycloalkyl, (C₃-C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(C,-C₆) alkyl or heteroaryl(C C₆)alkyl of R^5g and R^5h is optionally substituted with one or more groups independently selected from hydroxy, carboxy, and NR^5mR⁵ⁿ; each R^5j is independently selected from H, (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C6)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(Ci-Ce) alkyl and heteroaryl(Ci-C₆)alkyl;

each R^5k is independently selected from (d-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(C C₆) alkyl and heteroaryl(Ci-C₆)alkyl;

each R^5m and R⁵ⁿ is independently selected from H, (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C6)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(Ci-C6) alkyl and heteroaryl(Ci-C₆) alkyl; or R^5m and R⁵ⁿ together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino;

each R^5s is independently trifluoromethyl, trifluoromethoxy, aryl, or heteroaryl, wherein each aryl and heteroaryl is optionally substituted with one or more (Ci-C₆)alkyl, halo, hydroxy, cyano, nitro, (C]-C6)alkoxy, (C₃-C₆)cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^5gR^5h, -N(R^5j)S(0)₂R^5k, trifluoromethyl, trifluoromethoxy, -N⁺(R^5a)₃ D^", -C(=NR^5b)-NR^5cR^5d, -NR^5e- C(=NR^5b)-NR^5cR^5d and -NR^5gR^5h;

each R^5u and R^5v is independently selected from H and (C]-C6)alkyl;

each R^5x is independently selected from (Ci-C6)alkyl, (Ci-C₆)alkanoyl, and

-C(=0)NR^5uR^5v;

each R^5y is independently selected from H and (Ci-Cejalkyl; and

each D^" is independently a counter anion;

or a salt or prodrug thereof.

30. The compound of claim 28 wherein:

X is N or C(R^56');

W is N; R⁵¹ is absent; and A^" is absent; or

W is N; R⁵¹ is (Ci-C₆)alkyl, aryl, or aryl(C]-C6)alkyl; and A^" is counter anion; or W is C; R⁵¹ is hydrogen or -NR^5aaR^5bb and A^" is absent; or

W is C; R⁵¹ is -N⁺(R^5cc)₃; and A^" is counter anion;

Y is N; R⁵² is absent; and B^" is absent; or

Y is N; R⁵² is (Ci-Ce)alkyl, aryl, or aryl(Ci-C6)alkyl; and B^" is counter anion; or

Y is C; R⁵² is hydrogen or -NR^5ddR^5ee; and B^" is absent; or

Y is C; R^52' is -N⁺(R^5fr)₃; and B^" is counter anion;

any adjacent R⁶, R⁷, R⁵³ , R⁵⁴ and R⁵⁵ taken together can optional ly^{^}be methylenedioxy and each remaining R⁶, R⁷, R⁵³ , R⁵⁴ and R^55' is independently selected from H and Z-R^5x;

R⁸ is hydrogen, (C]-C6)alkyl, aryl, or aryl(Ci-C6)alkyl wherein each (Ci-C₆)alkyl of R⁸ is optionally substituted with one or more groups independently selected from halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, (C₃-C₆)cycloalkyl, oxo, carboxy, aryloxy, sulfo, and -NR^5gR^5h, and wherein each aryl of R⁸ is optionally substituted with one or more groups independently selected from (Ci-C₆)alkyl, halo, hydroxy, cyano, nitro, (C C6)alkoxy, (C3-C₆)cycloalkyl, carboxy, aryloxy, nitro, R^5s, and -NR^5gR^5h;

each Z is independently selected from -0-, -S-, and -N(R^5y)-;

at least one of R³, R⁴, R⁵, and R⁵⁶ is selected from hydroxy, carboxy, cyano, CF3SO3-, (C C₆)alkyl, (C₂-C₆)alkenyl, (C₂-C₆)alkynyl, (C_rC₆)alkoxy, (C₃-C₆)cycloalkyl, aryl(C_rC₆)alkyl, aryl, heteroaryl, heteroaryl(Ci-C6)alkyl, arylalkanoyl, and heteroarylalkanoyl; and the remainder ofR³, R⁴, R⁵, and R^56' are independently selected from H, hydroxy, carboxy, cyano, CF3SO₃-, (Ci-C₆)alkyl, (C₂-C₆)alkenyl, (C₂-C₆)alkynyl, (C C₆)alkoxy, (C₃-C₆)cycloalkyl, aryl(C_rC₆)alkyl, aryl, heteroaryl, heteroaryl(C_!-C₆)alkyl, aryl(Ci-C₆)alkanoyl, and heteroaryl(Ci-C₆)alkanoyl; wherein each (C_rC₆)alkyl, (C₂-C₆)alkenyl, (C₂-C₆)alkynyl, (CrC₆)alkoxy, (C₃-C₆)cycloalkyl, and (C]-C₆)alkanoyl of R³, R⁴, R⁵, and R⁵⁶ is optionally substituted with one or more groups independently selected from halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, (C₃-C₆)cycloalkyl, oxo, carboxy, aryloxy, sulfo, -S(0)₂NR^5gR^5h, -N(R^5j)S(0)₂R^5k, and -NR^5gR^5h; and wherein each aryl and heteroaryl of R³, R⁴, R⁵, and R⁵⁶ is optionally substituted with one or more groups independently selected from (C)-C₆)alkyl, halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, (C₃- C₆)cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^5gR^5h, -N(R^5j)S(0)₂R^5k, R^5s, and - NR^5gR^5h;

each R^5g and R^5h is independently selected from H, (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C₆)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(Ci-C₆) alkyl and heteroaryl(Ci-C6) alkyl; or R^5g and R^5h together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino;

each R^5j is independently selected from H, (Ci-C₆)alkyl, (C₃-C6)cycloalkyl, (C3- C6)cycloalkyl(Ci-C₆)alkyl, aryl, heteroaryl, aryl(Ci-Ce) alkyl and heteroaryl (Ci-Ce)alky];

each R^5k is independently selected from (C]-C₆)alkyl, (C₃-C₆)cycloalkyl, (C₃- C6)cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(Ci-Ce) alkyl and heteroaryl(Ci-C6)alkyl;

each R^5s is independently trifluoromethyl, trifiuoromethoxy, or aryl optionally substituted with one or more (Ci-C₆)alkyl, halo, hydroxy, cyano, nitro, (Ci-Ce)alkoxy, (C₃-C₆)cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^5gR^5h, -N(R^5j)S(0)₂R^5k, trifluoromethyl,

trifiuoromethoxy, and -NR^5gR^5h;

each R^5u and R^5v is independently selected from H and (Ci-C₆)alkyl;

each R^5x is independently selected from (Ci-C6)alkyl, (Ci-C₆)aIkanoyl, and

-C(=0)NR^5uR^5v; each R ^y is independently selected from H and (C]-C6)alkyl;

each R^5aa and R^5bb is independently selected from H and (d-C₆)alkyl; or R^5aa and R^5bb together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino;

each R^5cc is independently selected from H and (Ci-C6)alkyl

each R^5dd and R^ee is independently selected from H and (d-C₆)alkyl; or R^5ddand R^5ee together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; and

each R^5ff is independently selected from H and (Ci-C6)alkyl

or a salt or prodrug thereof.

31. The compound of claim 30 which is a compound of formula (Vb):

(Vb)

wherein Y is N; R⁵² is (Ci-C6)alkyl, aryl, or aryl(Ci-C₆)alkyl; and B^" is counter anion; Y is C; R⁵² is -N(R^5ff)₃; and B^" is counter anion;

or a salt or prodrug thereof.

The compound of claim 30 which is a compound of formula (Vc):

wherein R is (Ci-C₆)alkyl, aryl, or aryl(C) -C6)alkyl; and A^" is counter anion;

Y is N; and R⁵² is absent; or

Y is C; and R^2' is hydrogen or -NR^5ddR^5ee;

or a salt or prodrug thereof. The compound of claim 2 which is a compound of formula (Vd):

(Vd)

wherein R⁵¹ is hydrogen or -NR^5aaR^3DD;

Y is N; R⁵² is (Ci-C6)alkyl, aryl, or aryl(Ci-Ce)alkyl; and B^" is counter anion

Y is C; R⁵² is -N(R^5fr)₃; and B^~ is counter anion;

or a salt or prodrug thereof.

The compound of claim 2 which is a compound of formula (Ve):

wherein R is -N(R and A^" is counter anion

Y is N; and R⁵² is absent; or

Y is C; and R^52' is hydrogen or -NR^5ddR^5ee;

or a salt or prodrug thereof.

The compound of claim 2 which is a compound of formula

wherein W is N; R⁵¹ is (Ci-Ce)alkyl, aryl, or aryl(Ci-Ce)alkyl; and A^" is counter anion; or W is C; R⁵¹ is -N(R^5cc)₃; and A^" is counter anion;

or a salt or prodrug thereof. The compound of claim 2 which is a compound of formula (Vg):

(Vg)

wherein W is N; and R is absent; or

W is C; and R⁵¹ is hydrogen or -NR^5aaR^5bb; and

R⁵² is (Ci-C6)alk l, aryl, or aryl(C)-C6)alkyl; and B^" is counter anion;

or a salt or prodrug thereof.

The compound of claim 2 which is a compound of formula (Vh):

wherein W is N; R is (Ci-C₆)alkyl, aryl, or aryl(Ci-C6)alkyl; and A^" is counter anion; or W is C; R⁵¹ is -N(R^5cc)3; and A^" is counter anion; and

R^2' is hydrogen or -NR^5ddR^5ee;

or a salt or prodrug thereof.

38. The compound of claim 2 which is a compound of formula (Vj):

wherein W is N; and R is absent; or

W is C; and R⁵¹ is hydrogen or -NR^5aaR^5bb; R⁵² is -N(R^5fF)₃; and B^" is counter anion;

or a salt or prodrug thereof.

The compound of claim 1 which is a compound of formula (Vk)

or a salt or prodrug thereof.

40. The compound of claim 1 1 wherein at least one of Rv^3', ⁵R⁴ , and R⁵⁵ is -N⁺(R^5a)₃ D^", -C(=NR^5b)-NR^5cR^5d, -NR^5e-C(=NR^5b)-NR^5cR^5d, -NR^5gR^5h, or (d-C₆)alkyl that is substituted with one or more groups independently selected from -C(=NR^5b)-NR^5cR^5d, -NR ^e-C(=NR^5b)- NR^5cR^5d, and -NR^5gR^5h.

41. The compound of cl rmula (Vm):

(Vm)

or a salt or prodrug thereof.

42. The compound of claim 13 wherein R⁵² is hydrogen, -N⁺(R^5a)₃ D^", -C(=NR^5b)-NR^5cR^5d, -NR^5e-C(=NR^5b)-NR^5cR^5d, -NR^5gR^5h, or (CrC₆)alkyl that is substituted with one or more groups independently selected from -C(=NR^5b)-NR^5cR^5d, -NR^5e-C(=NR^5b)-NR^5cR^5d, and -NR^5gR^5h.

43. The compound of claim 13 wherein R⁵² is -C(=NR^5b)-NR^5cR^5d, -NR^5e-C(=NR^5b)- NR^5cR^5d, -NR^5gR^5h, or (Ci-C₆)alkyl that is substituted with one or more groups independently selected from -C(=NR^5b)-NR^5cR^5d, -NR^5e-C(=NR^5b)-NR^5cR^5d, and -NR^5gR^5h.

44. The compound of claim 13 wherein at least one of R^52', R⁵³ , R^54', and R⁵⁵ is -N⁺(R⁵ )₃ D\ -C(=NR^5b)-NR^5cR^5d, -NR^5e-C(=NR^5b)-NR^5cR^5d, -NR^5g5R^h, or (d-C₆)alkyl that is substituted with one or more groups independently selected from -C(=NR^5b)-NR^5cR , -NR -C^NR⁵")- NR^5cR^5d, and -NR^5eR^5h.

45. The compound of claim 1 which is a compound of formula (Vn):

or a salt or prodrug thereof.

46. The compound of claim 17 wherein at least one of R^S1, R⁵³ , R⁵⁴ , and R⁵⁵ is -N⁺(R^5a)₃ D\ -C(=NR^5b)-NR^5cR^5d, -NR^5e-C(=NR^5b)-NR^5cR^5d, -NR^5gR^5h, or (C C₆)aIkyI that is substituted with one or more groups independently selected from -C(=NR^5b)-NR^5cR^5d, -NR^5e-C(=NR^5b)- NR^5cR^5d, and -NR^SgR^5h.

47. The compound of claim 1 which is a compound of formula (Vo):

or a salt or prodrug thereof.

48. The compound of claim 19 wherein at least one of R⁵¹, R⁵² , R⁵³ , R⁵⁴ , and R⁵⁵ is -N⁺(R^5a)₃ D^", -C(=NR^5b)-NR^5cR^5d, or -NR^5e-C(=NR^5b)-NR^5cR^5d, -NR^5gR^5h, or (C_!-C₆)alkyl that is substituted with one or more groups independently selected from -C(=NR^5b)-NR^5cR^S , -NR^5e- C(=NR^5b)-NR^5cR^5d, and -NR^5gR^5h.

49. The compound of any one of claims 29-48 wherein R³ is phenyl, benzyl, biphenyl, cyclopropyl, or furyl.

50. The compound of any one of claims 29-48 wherein R⁴ is phenyl, biphenyl, cyclopropyl, or furyl.

51. The compound of any one of claims 29-48 wherein R⁵ is phenyl, biphenyl, cyclopropyl, or furyl.

52. The compound of any one of claims 29-48 wherein R⁵⁶ is phenyl, benzyl, biphenyl, cyclopropyl, or furyl.

53. The compound of claim 29 wherein W is N; and R⁵¹ is methyl.

54. The compound of claim 29 wherein W is C and R^SI is hydrogen.

55. The compound of claim 29 wherein W is C and R⁵¹ is-NR⁶R^h.

56. The compound of claim 29 wherein W is C and R⁵¹ is -N⁺(R^a)₃ D^".

57. The compound of claim 29 wherein Y is N and R⁵² is methyl.

58. The compound of claim 29 wherein Y is C and R⁵² is hydrogen.

59. The compound of claim 29 wherein Y is C and R⁵² -NR⁸R^h.

60. The compound of claim 29 wherein Y is C and R⁵² is -N⁺(R^a)₃ D^".

61. The compound of any one of claims 29-60 wherein at least one Z is -0-.

62. The compound of any one of claims 29-60 wherein at least one Z is -S-.

63. The compound of any one of claims 29-60 wherein at least one Z is -N(R^5y)-.

64. The compound of any one of claims 29-60 wherein each Z is -0-.

65. The compound of any one of claims 29-60 wherein each Z is -S-.

66. The compound of any one of claims 29-60 wherein each Z is -N(R^5y)-.

67. The compound of any one of claims 29-60 wherein R^5x is (C_rC6)alkyl.

6 7 53 ' 54^* 5 '

68. The compound of any one of claims 29-60 wherein R , R , R , R and R are each independently (C]-C3)alkoxy.

69. The compound of any one of claims 29-60 wherein R , R , R , R and R are each methoxy.

70. The compound of any one of claims 29-60 wherein R⁶ is (Ci-C3)alkoxy.

71. The compound of any one of claims 29-60 wherein R⁶ is methoxy.

72. The compound of any one of claims 29-60 and 70-71 wherein R⁷ is (Ci-C₃)alkoxy.

73. The compound of any one of claims 29-60 and 70-71 wherein R⁷ is methoxy.

74. The compound of any one of claims 29-60 and 70-73 wherein R⁵³ is (Ci-C₃)alkoxy.

75. The compound of any one of claims 29-60 and 70-73 wherein R⁵³ is methoxy.

76. The compound of any one of claims 29-60 and 70-75 wherein R⁵⁴ is (Ci-C₃)alkoxy.

77. The compound of any one of claims 29-60 and 70-75 wherein R⁵⁴ is methoxy.

78. The compound of any one of claims 29-60 and 70-77 wherein R⁵⁵ is (Ci-C₃)alkoxy.

79. The compound of any one of claims 29-60 and 70-77 wherein R⁵⁵ is methoxy.

80. The compound of any one of claims 29-60 wherein R⁶, R⁷, R^53', and R⁵⁴ are each methoxy.

81. The compound of any one of claims 29-60 wherein R⁶, R⁷, R⁵⁴ , and R⁵⁵ are each methoxy.

82. The compound of any one of claims 29-60 wherein R⁶ and R⁷ taken together are methylenedioxy.

83. The compound of any one of claims 29-60 wherein R⁵³ and R⁵⁴ taken together are methylenedioxy.

84. The compound of any one of claims 2960 wherein R⁵⁴ and R⁵⁵ taken together are methylenedioxy.

85. The compound of any one of claims 29-84 wherein each R^5s is independently trifluoromethyl, trifluoromethoxy, or aryl optionally substituted with one or more (C)-C6)alkyl, halo, hydroxy, cyano, nitro, (d-C6)alkoxy, (C3-C₆)cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^5gR^5h, -N(R^j)S(0)₂R^5k, trifluoromethyl, trifluoromethoxy, and -NR^5gR^5h;

86. The compound of claim 29 which is:

wherein R⁵⁴ and R⁵ are each H or methoxy, or taken together are methylenedioxy; or a salt or prodrug thereof.

87. The compound of claim 29 which is:

wherein R⁵⁴ and R^55' are each H or methoxy, or taken together are methylenedioxy; or a salt or prodrug thereof.

88. The compound of claim 29 which is:

89. The compound of claim 29 which is:

wherein R⁵⁴ and R⁵⁵ are each H or methoxy, or taken together are methylenedioxy; or a salt or prodrug thereof.

90. The compound of claim 29 which is:

wherein R⁵⁴ and R⁵⁵ are each H or methoxy, or taken together are methylenedioxy; or a salt or prodrug thereof.

91. The compound of claim 29 which is:

wherein R⁵⁴ and R⁵⁵ are each H or methoxy, or taken together are methylenedioxy; or a salt or prodrug thereof.

92. The compound of claim 29 which is:

wherein R⁵⁴ and R^55' are each H or methoxy, or taken together are methylenedioxy; or a salt or prodrug thereof.

93. The compound of claim 29 which is:

wherein R⁵⁴ and R⁵⁵ are each H or methoxy, or taken together are methylenedioxy; or a salt or prodrug thereof.

94. The compound of claim 29 which is:

wherein R⁵⁴ and R⁵⁵ are each H or methoxy, or taken together are methylenedioxy; or a salt or prodrug thereof.

95. The compound of claim 29 which is:

or a salt or prodrug thereof.

96. The compound of claim 29 wherein D^" is CI^", Br^", Γ, CF3SO3^", malate, fumarate, formate, tosylate, methanesulfonate, acetate, citrate, malonate, tartrate, succinate, benzoate, ascorbate, a- ketoglutarate, or a-glycerophosphate.

97. The compound of claim 29 wherein at least one of least one W, X, Y, R¹, R⁵² , R⁵³ , R^54', R⁵⁵ , and R⁵⁶ comprises at least one nitrogen atom.

98. The compound of claim 1 wherein:

X is ^(R^XR⁸²) B^";

Y is C(R⁸³);

A is N or C-R^4';

any adjacent R⁶, R⁷, R⁸, R⁴ and R⁵ taken together can optionally be methylenedioxy and each remaining R⁶, R⁷, R⁸, R⁴ and R⁵ is independently selected from H, R^bb, and Z-R^x;

each Z is independently selected from -0-, -S-, and -N(R^y)-; at least one of R⁴, R⁵, R² , R³ , and R⁶ is selected from hydroxy, carboxy, cyano,

CF3SO3-, (C,-C₆)alkyl, (C₂-C₆)alkenyl, (C₂-C₆)alkynyl, (d-C₆)alkoxy, cycloalkyl, aryl(C C₆)alkyl, aryl, heteroaryl, heteroaryl(Ci-Ce)alkyl, arylalkanoyl, and heteroarylalkanoyl; and the remainder of R⁴, R⁵, R² , R³ , and R⁶ are independently selected from hydrogen, halo, hydroxy, carboxy, cyano, CF3SO3-, (C C₆)alkyl, (C₂-C₆)alkenyl, (C₂-C₆)alkynyl, (Q-Ce^lkoxy, cycloalkyl, aryl(Ci-C6)alkyl, aryl, heteroaryl, heteroaryl(Ci-C6)alkyl, aryl(CrC6)alkanoyl, and heteroaryl(C_rC₆)alkanoyl; or R^6' and R¹⁰ taken together are -(CR¹³₂)₂- or -CR¹⁴=CR¹⁴-;

wherein each (C₁-C₆)alkyl, (C₂-Ce)alkenyl, (C₂-C₆)alkynyl, (Ci-C₆)alkoxy, cycloalkyl, and (Ci- C₆)alkanoyl of R⁴, R⁵, R² , R³ , and R⁶ is optionally substituted with one or more groups independently selected from halo, hydroxy, cyano, nitro, (C_rC₆)alkoxy, cycloalkyl, oxo, carboxy, aryloxy, sulfo, -S(0)₂NR^gR^h, -N(R^j)S(0)₂R^k, and -NR^gR^h; and wherein each aryl, and heteroaryl of R⁴, R⁵, R² , R³ , and R⁶ is optionally substituted with one or more groups independently selected from (Ci-C₆)alkyl, halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, R³², -S(0)₂NR⁸R^h, -N(R^j)S(0)₂R^k, and -NR^gR^h;

the bond represented by— is present and R⁸² is absent except as defined below when R⁸¹ and R^8a taken together with the atoms to which they are attached form a 5- or 6-membered heterocyclic ring or a 5- or 6-membered heteroaryl ring;

R⁸¹ is absent and B^" is absent; or R⁸¹ is H or and B^" is counterion;

or R⁸¹ and R^8a taken together with the atoms to which they are attached form a 5- or 6- membered heterocyclic ring or a 5- or 6-membered heteroaryl ring, wherein a) when the bond represented by— is present in the 5- or 6-membered heterocyclic ring or the 5- or 6-membered heteroaryl ring, R⁸² is absent and B^" is a counterion, b) when the bond represented by— is absent in the 5- or 6-membered heterocyclic ring or the 5- or 6-membered heteroaryl ring, R⁸² is (Ci-C₆)alkyl and B^" is a counterion, or c) when the bond represented by— is absent in the 5- or 6-membered heterocyclic ring or the 5- or 6-membered heteroaryl ring, R⁸² is absent and B^" is absent;

R⁸³ is H, (Ci-C₆)alkyl, (Ci-C₆)alkoxy, (d-C₆)alkylthio, aryloxy, arylthio, -NR^8aR^8b or cyano; or R⁶ and R⁸³ taken together are -(CR¹³₂)₂- or -CR¹⁴=CR¹⁴-;

each R¹³ is independently H, (Ci-C6)alkyl, (C]-C6)alkoxy, (C]-C6)alkylthio, aryloxy or arylthio wherein any (C₁-C6)alkyl, (Q-Ceialko y, and (CrC6)alkylthio of R¹³ is optionally substituted with one or more groups selected from halo, cyano, oxo (=0), (Cj-C₆)alkyl, (C₃- C₆)cycloalkyl, carboxy, N0₂, hydroxy, (Ci-C6)alkoxy, (Ci-C6)alkoxycarbonyl, (Ci- C₆)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, and -NR^8eR^8f, and wherein any aryloxy, or arylthio of R¹³ is optionally substituted with one or more groups selected from halo, cyano, (Ci-C₆)alkyl, (C₃-C₆)cycloalkyl, carboxy, N0₂, hydroxy, (Ci-C₆)alkoxy, (Ci-C₆)alkoxycarbonyl, (C]-C6)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, and -NR^8eR^8f;

each R¹⁴ is independently H, (C)-C6)alkyl, (Ci-C6)alkoxy, (Ci-C6)alkylthio, aryloxy or arylthio wherein any (CrC₆)alkyl, (Ci-C₆)alkoxy, and (Ci-C₆)alkylthio of R¹⁴ is optionally substituted with one or more groups selected from halo, cyano, oxo (=0), (Ci-C6)alkyl, (C₃- C₆)cycloalkyl, carboxy, N0₂, hydroxy, (Ci-C6)alkoxy, (C C6)alkoxycarbonyl, (Q- C₆)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, and -NR^8eR^8f, and wherein any aryloxy, or arylthio of R¹⁴ is optionally substituted with one or more groups selected from halo, cyano, (Ci-C6)alkyl, (C3-C₆)cycloalkyl, carboxy, N0₂, hydroxy, (Ci-C6)alkoxy, (Cj-C6)alkoxycarbonyl, (Ci-C₆)alkanoyloxy, aryl, heteroaryl, aryloxy, heteroaryloxy, and -NR^8eR^8f;

R^8a is hydrogen, (Ci-C6)alkyl, aryl, aryl(C]-C6)alkyl, heteroaryl, or heteroaryl(Ci- C6)alkyl; wherein each (Ci-C₆)alkyl of R^8a is optionally substituted with one or more groups selected from halo, hydroxy, cyano, nitro, (CrC6)alkoxy, cycloalkyl, oxo, carboxy, -NR^8gR^8h, and aryloxy, and wherein each aryl and heteroaryl of R^8a is optionally substituted with one or more groups selected from (Ci-Ce)alkyl, halo, hydroxy, cyano, nitro, (Ci-Ce)alkoxy, cycloalkyl, carboxy, -NR^8gR^8h, and aryloxy;

R^8b is hydrogen, (C_rC₆)alkyl, aryl, ai l(Ci-C₆)alk l, heteroaryl, heteroaryl(C C₆)alkyl, -C(=0)-R^8m, -C(=0)-OR⁸ⁿ, -C(=0)-SR^8p, -C(=0)-NR^8qR^8r, -C(=S)-R^8m, -C(=S)-OR⁸ⁿ,

-C(=S)-SR^8p, -C(=S)-NR^8qR ^r, or -C(=NR^8c)-R^8d; wherein each (C,-C₆)alkyl of R^8b is optionally substituted with one or more groups independently selected from halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, cycloalkyl, oxo, carboxy, and aryloxy; and wherein each aryl, and heteroaryl of R^b is optionally substituted with one or more groups independently selected from (C₁-C6)alkyl, halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, cycloalkyl, carboxy, and aryloxy; or R^8aand R^8b taken together with the nitrogen to which they are attached form aziridino, azetidino, morpholino, piperazino, pyrrolidino, pyrrole, indole, or piperidino, which aziridino, azetidino, morpholino, piperazino, pyrrolidino pyrrole, indole, or piperidino can optionally be substituted with one or more (C]-C6)alkyl;

R^8c is hydrogen, (C]-C₆)alkyl, aryl, or heteroaryl;

R^8d is hydrogen, (C C₆)alkyl, (C_rC₆)alkoxy, (C,-C₆)alkylthio, (d-C₆)alkanoyl, or -NR^eR^f;

R⁸ and R^8f are each independently selected from H, (Ci-C6)alkyl, cycloalkyl, cycloalkyl(CrC6)alkyl, aryl, heteroaryl, aryl(Ci-C₆)alkyl and heteroaryl(Ci-Ce)alkyl; or R^8e and R^8f together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; each R^8g and R^8h is independently selected from H, (Ci-C6)alkyl, cycloalkyl,

cycloalkyl(Ci-C6)alkyl, aryl, heteroaryl, aryl(Ci-C6)alkyl and heteroaryl(Ci-C6)alkyl; or R^8gand R^8h together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino;

each R^8j is independently selected from H, (C₁-Ce)alkyl, cycloalkyl, cycloalkyl(C!- C₆)alkyl, aryl, heteroaryl, aryl(Ci-C6)alkyl and heteroaryl(C]-C6)alkyl;

each R^8k is independently selected from (Ci-C6)alkyl, cycloalkyl, cycloalkyl(C₁-C₆)alkyl, aryl, heteroaryl, aryl(Ci-C6)alkyl and heteroaryl(Ci-C6)alkyl;

each ⁸R^m is independently selected from H, (Ci-Ce)alkyl, cycloalkyl, cycloalkyl(C]- C₆)alkyl, aryl, heteroaryl, aryl(C)-C6)alkyl and heteroaryl(Ci-Ce)alkyl;

each R⁸ⁿ is independently selected from H, (Ci-C6)alkyl, cycloalkyl, cycloalkyl (C]- C6)alkyl, aryl, heteroaryl, aryl(C]-C6)alkyl and heteroaryl(Ci-C₆)alkyl, wherein each aryl, and heteroaryl is optionally substituted with one or more groups independently selected from (Q- C₆)alkyl, halo, hydroxy, cyano, nitro, (Ci-C6)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8gR^8h, -N(R^8J)S(0)₂R^8k, and -NR^8gR^8h;

each R^8p is independently selected from H, (C]-C6)alkyl, cycloalkyl, cycloalkyl(C_r

C6)alkyl, aryl, heteroaryl, aryl(C]-C6)alkyl and heteroaryl(C!-C6)alkyl, wherein each aryl, and heteroaryl is optionally substituted with one or more groups independently selected from (Q- C₆)alkyl, halo, hydroxy, cyano, nitro, (C₁-C₆)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h;

each R^8q is independently selected from H, (C]-C6)alkyl, cycloalkyl, cycloalkyl(C]- C₆)alkyl, aryl, heteroaryl, aryl(Ci-C6)alkyl and heteroaryl(Ci-C6)alkyl; and each R^8r is independently selected from H, (Ci-C6)alkyl, cycloalkyl, cycloalkyl(CrC6)alkyl, aryl, heteroaryl, aryl(C]-C6)alkyl and heteroaryl(Ci-C₆)alkyl; or R^8q and R^8r together with the nitrogen to which they are attached form a aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino; each R^8u and R^8v is independently selected from H and (Ci-C6)alkyl;

each R^8x is independently selected from (Ci-Ce)alkyl, (CrC₆)alkanoyl, and

-C(=0)NR^8uR^8v;

each R^8y is independently selected from H and (Ci-Cejalkyl;

each R^8aa is independently selected from aryl and heteroaryl, which aryl and heteroaryl is optionally substituted with one or more groups independently selected from (C] -C6)alkyl, halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; and

each R is independently selected from aryl and heteroaryl, which aryl and heteroaryl is optionally substituted with one or more groups independently selected from (Ci-C6)alkyl, halo, hydroxy, cyano, nitro, (C]-C6)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h;

or a salt thereof.

99. The compound of claim 98 wherein R⁸³ is H, (Ci-C₆)alkyl, (Ci-C₆)alkoxy, (Q- Ce)alkylthio, aryloxy, arylthio, -NR^8aR^8b or cyano.

100. The compound of claim 98 wherein R⁸³ is H, (Ci-C₆)alkyl, (d-C₆)alkoxy, (C

C₆)alkylthio, aryloxy, or arylthio.

101. The compound of claim 98 wherein R⁸³ is -NR^8aR^8b or cyano.

102. The compound of claim 98 wherein R⁶ and R⁸³ taken together are -(CR¹³₂)₂- or

-CR^, =CR¹⁴-.

103. The compound of any one of claims 98-102 wherein the bond represented by— is present and R⁸² is absent.

104. The compound of any one of claims 98-99 wherein R⁸¹ and R⁸ taken together with the atoms to which they are attached form a 5- or 6-membered heterocyclic ring or a 5- or 6- membered heteroaryl ring.

105. The compound of any one of claims 98-103 wherein R is absent and B^" is absent.

106. The compound of any one of claims 98-103 wherein R⁸¹ is H or (Ci-C₆)alkyl and Ε is a counterion.

107. The compound of any one of claims 98-102 which is a compound of formula (Villa):

wherein R⁶ is is selected from hydroxy, carboxy, cyano, CF3SO3-, (Ci-C6)alkyl, (C₂-C6)alkenyl, (C₂-C6)alkynyl, (C]-C₆)alkoxy, cycloalkyl, aryl(Ci-C₆)alkyl, aryl, heteroaryl, heteroaryl(Ci- C₆)alkyl, arylalkanoyl, and heteroarylalkanoyl; wherein each (C]-C6)alkyl, (C₂-C6)alkenyl, (C₂- C₆)alkynyl, (C|-C6)alkoxy, cycloalkyl, and (CpC6)alkanoyl of R⁶ is optionally substituted with one or more groups independently selected from halo, hydroxy, cyano, nitro, (C_\-C )alkoxy, cycloalkyl, oxo, carboxy, aryloxy, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; and wherein each aryl, and heteroaryl of R⁶ is optionally substituted with one or more groups independently selected from (C₁-C6)alkyl, halo, hydroxy, cyano, nitro, (C C6)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, R^8aa, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; or a salt thereof.

108. The compound of any one of claims 98-106 which is a compound of formula (Vlllb):

wherein R³ is is selected from hydroxy, carboxy, cyano, CF3SO3-, (Cj-C6)alkyl, (C₂-C₆)alkenyl, (C₂-C₆)alkynyl, (Q-Ceialkoxy, cycloalkyl, aryl(Ci-C₆)alkyl, aryl, heteroaryl, heteroaryl(C C6)alkyl, arylalkanoyl, and heteroarylalkanoyl; wherein each (Ci-C₆)alkyl, (C₂-C₆)alkenyl, (C₂- C₆)alkynyl, (Ci-C6)alkoxy, cycloalkyl, and (Ci-C₆)alkanoyl of R³ is optionally substituted with one or more groups independently selected from halo, hydroxy, cyano, nitro, (Ci-Ce)alkoxy, cycloalkyl, oxo, carboxy, aryloxy, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; and wherein each aryl, and heteroaryl of R³ is optionally substituted with one or more groups independently selected from (Ci-C6)alkyl, halo, hydroxy, cyano, nitro, (C C₆)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, R^8aa, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; or a salt thereof.

109. The compound of any one of claims 98-106 which is a compound of formula (VIIIc):

wherein R² is is selected from hydroxy, carboxy, cyano, CF₃SO₃-, (Ci-C6)alkyl, (C₂-C₆)alkenyl, (C₂-C6)alkynyl, (Ci-C₆)alkoxy, cycloalkyl, aryl(Ci-C₆)alkyl, aryl, heteroaryl, heteroaryl(C)- C₆)alkyl, arylalkanoyl, and heteroarylalkanoyl; wherein each (Ci-C₆)alkyl, (C₂-Ce)alkenyl, (C₂- C₆)alkynyl, (CrC₆)alkoxy, cycloalkyl, and (C₁-C₆)alkanoyl of R² is optionally substituted with one or more groups independently selected from halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, cycloalkyl, oxo, carboxy, aryloxy, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; and wherein each aryl, and heteroaryl of R² is optionally substituted with one or more groups independently selected from (Ci-Cejalkyl, halo, hydroxy, cyano, nitro, (C]-C₆)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, R^8aa, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; or a salt thereof.

110. The compound of any one of claims 98-106 which is a compound of formula (Vllld):

(Vllld) wherein R⁴ is is selected from hydroxy, carboxy, cyano, CF3SO3-, (Ci-Cejalkyl, (C₂-Ce)alkenyl, (C₂-C₆)alkynyl, (d-Ceialkoxy, cycloalkyl, aryl(Ci-Ce)alkyl, aryl, heteroaryl, heteroaryl(Ci- Cejalkyl, arylalkanoyl, and heteroarylalkanoyl; wherein each (Ci-Cejalkyl, (C₂-C6)alkenyl, (C₂- C6)alkynyl, (Ci-C6)alkoxy, cycloalkyl, and (Ci-C6)alkanoyl of R⁴ is optionally substituted with one or more groups independently selected from halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, cycloalkyl, oxo, carboxy, aryloxy, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; and wherein each aryl, and heteroaryl of R⁴ is optionally substituted with one or more groups independently selected from (Ci-C₆)alkyl, halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, R^8aa, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; or a salt thereof.

111. The compound of any one of claims 98-106 which is a compound of formula (Vllle):

wherein R⁵ is is selected from hydroxy, carboxy, cyano, CF3SO3-, (Ci-Cejalkyl, (C₂-C6)alkenyl, (C₂-C₆)alkynyl, (C₁-C₆)alkoxy, cycloalkyl, aryl(C₁-C₆)alkyl, aryl, heteroaryl, heteroaryl(Ci- C₆)alkyl, arylalkanoyl, and heteroarylalkanoyl; wherein each (Ci-C6)alkyl, (C₂-C₆)alkenyl, (C₂- C6)alkynyl, (Cj-C6)alkoxy, cycloalkyl, and (Ci-C6)alkanoyl of R⁵ is optionally substituted with one or more groups independently selected from halo, hydroxy, cyano, nitro, (Ci-Ce)alkoxy, cycloalkyl, oxo, carboxy, aryloxy, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; and wherein each aryl, and heteroaryl of R⁵ is optionally substituted with one or more groups independently selected from (Ci-C₆)alkyl, halo, hydroxy, cyano, nitro, (Ci-Ce)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, R^8aa, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; or a salt thereof.

112. The compound of any one of claims 98-111 wherein at least one Z is -0-.

113. The compound of any one of claims 98-111 wherein at least one Z is -S-.

The compound of any one of claims 98-111 wherein at least one Z is -N(R^8y)-

115. The compound of any one of claims 98-111 wherein each Z is -0-.

116. The compound of any one of claims 98-111 wherein each Z is -S-.

117. The compound of any one of claims 98-111 wherein each Z is -N(R^8y)-.

118. The compound of any one of claims 98-117 wherein R^8x is (C]-C₆)alkyl.

119. The compound of any one of claims 98-111 wherein R⁶, R⁷, R⁸, R⁴ and R⁵ are each independently (C₁-C3)alkoxy.

120. The compound of any one of claims 98-111 wherein R⁶, R⁷, R⁸, R⁴ and R⁵ are each methoxy.

121. The compound of any one of claims 98-111 wherein R⁶ is (CrC₃)alkoxy.

122. The compound of any one of claims 98-111 wherein R⁶ is methoxy.

123. The compound of any one of claims 98-111 and 121 - 122 wherein R⁷ is (C i -C₃)alkoxy.

124. The compound of any one of claims 98-111 and 121-122 wherein R⁷ is methoxy.

125. The compound of any one of claims 98-111 and 121-124 wherein R⁸ is (Ci-C₃)alkoxy.

126. The compound of any one of claims 98-111 and 121-124 wherein R⁸ is methoxy.

127. The compound of any one of claims 98-111 and 121-126 wherein R⁴ is (Ci-C₃)alkoxy.

128. The compound of any one of claims 98-111 and 121-126 wherein R⁴ is methoxy.

129. The compound of any one of claims 98-111 and 121-128 wherein R⁵ is (Ci-C₃)alkoxy.

130. The compound of any one of claims 98-111 and 121-128 wherein R⁵ is methoxy.

131. The compound of any one of claims 98-111 wherein R⁷, R⁸, R⁴ and R⁵ are each methoxy.

132. The compound of any one of claims 98-111 and 125-130 wherein R⁶ and R⁷ taken together are methylenedioxy.

133. The compound of any one of claims 98-111, 121, 124, and and 127-130 wherein R⁷ and R⁸ taken together are methylenedioxy.

134. The compound of any one of claims 98-105 and 121-126 wherein R⁴ and R⁵ taken together are methylenedioxy.

135. The compound of any one of claims 98-111 and 125-130 wherein R⁶ and R⁷ taken together are methylenedioxy and R⁴ and R⁵ taken together are methylenedioxy.

136. The compound of any one of claims 98-135 wherein R 83 is cyano.

137. The compound of any one of claims 98-135 wherein R⁸³ is -NR^aR^b.

138. The compound of claim 137 wherein R^8a is hydrogen or methyl.

139. The compound of claim 137 or 138 wherein R^8b is hydrogen, (Cj-C6)alkyl, aryl, aryl(Ci- C6)alkyl, heteroaryl, or heteroar liQ-Ceialkyl.

140. The compound of claim 137 or 138 wherein R^8b is hydrogen, methyl, phenyl, or benzyl.

141. The compound of claim 137 or 138 wherein R^8b is -C(=NR^8c)-R^8d.

142. The compound of claim 137 wherein R^8a and R^8b taken together with the nitrogen to which they are attached form aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino, which aziridino, azetidino, morpholino, piperazino, pyrrolidino or piperidino can optionally be substituted with one or more (CpCeJalkyl.

143. The compound of claim 141 wherein R^8c is hydrogen.

144. The compound of claim 141 or 142 wherein R is methyl or amino.

145. The compound of any one of claims 98-135 wherein R⁸³ is H.

146. The compound of claim 98 which is:

311

312

or a salt thereof.

147. The compound of claim 98 which is:

or a salt thereof.

148. The compound of claim 107 wherein R⁶ is selected from aryl and heteroaryl, which aryl, and heteroaryl of R⁶ is optionally substituted with one or more groups independently selected from (Ci-C₆)alkyl, halo, hydroxy, cyano, nitro, (CrC₆)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, R^8aa, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂⁸R^k, and -NR^8gR^8h; and each R^8aa is independently selected from aryl and heteroaryl, which aryl and heteroaryl is optionally substituted with one or more groups independently selected from (Ci-Ce)alkyl, halo, hydroxy, cyano, nitro, (Ci- C₆)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h.

149. The compound of claim 108 wherein R³ is selected from aryl and heteroaryl, which aryl, and heteroaryl of R³ is optionally substituted with one or more groups independently selected from (C]-C6)alkyl, halo, hydroxy, cyano, nitro, (Ci-C6)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, R^8aa, -S(0)₂NR^8gR^8h, -N(R^8J)S(0)₂R^8k, and -NR^8gR^8h; and each R^8aa is independently selected from aryl and heteroaryl, which aryl and heteroaryl is optionally substituted with one or more groups independently selected from (Ci-C6)alkyl, halo, hydroxy, cyano, nitro, (Cj- C₆)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h.

150. The compound of claim 109 wherein R² is selected from aryl and heteroaryl, which aryl, and heteroaryl of R² is optionally substituted with one or more groups independently selected from (Ci-C6)alkyl, halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, R^8aa, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; and each R^8aa is independently selected from aryl and heteroaryl, which aryl and heteroaryl is optionally substituted with one or more groups independently selected from (Ci-C₆)alkyl, halo, hydroxy, cyano, nitro, (Ci- C₆)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h.

151. The compound of claim 110 wherein R⁴ is selected from aryl and heteroaryl, which aryl, and heteroaryl of R⁴ is optionally substituted with one or more groups independently selected from (Ci-C₆)alkyl, halo, hydroxy, cyano, nitro, (C₁-Ce)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, R^8aa, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; and each R^8aa is independently selected from aryl and heteroaryl, which aryl and heteroaryl is optionally substituted with one or more groups independently selected from (Ci-C6)alkyl, halo, hydroxy, cyano, nitro, (Ci- C₆)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h.

152. The compound of claim 111 wherein R⁵ is selected from aryl and heteroaryl, which aryl, and heteroaryl of R⁵ is optionally substituted with one or more groups independently selected from (Ci-C₆)alkyl, halo, hydroxy, cyano, nitro, (Ci-Ce)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, R^8aa, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; and each R^8aa is independently selected from aryl and heteroaryl, which aryl and heteroaryl is optionally substituted with one or more groups independently selected from (Ci-C6)alkyl, halo, hydroxy, cyano, nitro, (Ci- C₆)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h.

153. The compound of claim 107 wherein R⁶ is selected from phenyl, pyridyl and furanyl and is optionally substituted with one or more groups independently selected from (Ci-C₆)alkyl, halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, R^8aa,

-S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; and each R^8aa is independently selected from aryl and heteroaryl, which aryl and heteroaryl is optionally substituted with one or more groups independently selected from (Ci-C6)alkyl, halo, hydroxy, cyano, nitro, (Cj-C6)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8g8R^h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h.

154. The compound of claim 108 wherein R³ is selected from phenyl, pyridyl and furanyl and is optionally substituted with one or more groups independently selected from (C]-C6)alkyl, halo, hydroxy, cyano, nitro, (Ci-Ce)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, R^8aa,

-S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; and each R^8aa is independently selected from aryl and heteroaryl, which aryl and heteroaryl is optionally substituted with one or more groups independently selected from (Ci-C6)alkyl, halo, hydroxy, cyano, nitro, (Q-C6)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h.

155. The compound of claim 109 wherein R² is selected from aryl and heteroaryl, which aryl, and heteroaryl of R² is optionally substituted with one or more groups independently selected from (Ci-C6)alkyl, halo, hydroxy, cyano, nitro, (Ci-C₆)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, R^8aa, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R⁸ , and -NR^8gR^8h; and each R^8aa is independently selected from aryl and heteroaryl, which aryl and heteroaryl is optionally substituted with one or more groups independently selected from (Ci-Ce)alkyl, halo, hydroxy, cyano, nitro, (Ci- C₆)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^gR^h.

156. The compound of claim 110 wherein R⁴ is selected from phenyl, pyridyl and furanyl and is optionally substituted with one or more groups independently selected from (C_rC6)alkyl, halo, hydroxy, cyano, nitro, (Ci-C6)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, R^8aa,

-S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; and each R^8aa is independently selected from aryl and heteroaryl, which aryl and heteroaryl is optionally substituted with one or more groups independently selected from (Ci-C6)alkyl, halo, hydroxy, cyano, nitro, (C]-C6)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8gR^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h.

157. The compound of claim 111 wherein R⁵ is selected from phenyl, pyridyl and furanyl and is optionally substituted with one or more groups independently selected from (Ci-C6)alkyl, halo, hydroxy, cyano, nitro, (Ci-Ce)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, R^8aa,

-S(0)₂NR^8ER^8h, -N(R^8j)S(0)₂R^8k, and -NR^8gR^8h; and each R^8aa is independently selected from aryl and heteroaryl, which aryl and heteroaryl is optionally substituted with one or more groups independently selected from (C)-C₆)alkyl, halo, hydroxy, cyano, nitro, (C₁-C₆)alkoxy, cycloalkyl, carboxy, aryloxy, nitro, sulfo, -S(0)₂NR^8gR^8h, -N(R^8J)S(0)₂R^8k, and -NR^8gR^8h.

158. The compound of claim 107 wherein R⁶ is selected from phenyl, pyridyl and furanyl and is optionally substituted with one or more groups independently selected from phenyl, pyridyl, -NR^8gR^8h, (C C₆)alkoxy, dimethylaminophenyl, and halo.

159. The compound of claim 108 wherein R³ is selected from phenyl, pyridyl and furanyl and is optionally substituted with one or more groups independently selected from phenyl, pyridyl, -NR^8gR^8h, (C C₆)alkoxy, dimethylaminophenyl, and halo.

160. The compound of claim 109 wherein R² is selected from phenyl, pyridyl and furanyl and is optionally substituted with one or more groups independently selected from phenyl, pyridyl, -NR^8gR^8h, (Ci-C₆)alkoxy, dimethylaminophenyl, and halo.

161. The compound of claim 110 wherein R⁴ is selected from phenyl, pyridyl and furanyl and is optionally substituted with one or more groups independently selected from phenyl, pyridyl, -NR^8gR^8h, (C C₆)alkoxy, dimethylaminophenyl, and halo.

162. The compound of claim 111 wherein R⁵ is selected from phenyl, pyridyl and furanyl and is optionally substituted with one or more groups independently selected from phenyl, pyridyl, -NR^8gR^8h, (Ci-Ce)alkoxy, dimethylaminophenyl, and halo.

163. The compound of claim 98 wherein at least one of R⁴, R⁵, R , R^3', and R^6' is selected from 3-biphenyl, 3-(4'-fluoro)biphenyl, 4-biphenyl, 4-(4'-fluoro)biphenyl, 3,5-bis(4- fluorophenyl)phenyl, 4-fluorophenyl, phenyl, 3-pyridyl, 4-pyridyl, 3-dimethylaminophenyl, 3- furanyl, 3-methoxyphenyl, 4-pyrid-3-ylphenyl, 4-pyrid-4-ylphenyl, 4-(3- dimethylaminophenyl)phenyl, 4-(3-furanyl)phenyl, 2-phenylpyrid-4-yl, 2-(3- methoxyphenyl)pyrid-3-yl, 2-phenylfur-4-yl, and 2-pyrid-4-yl)pyrid-5-yl.

164. The compound of any one of claims 98-163 wherein A is N.

165. The compound of any one of claims 98-163 wherein A is C-R⁴ .

166. The compound of claim 98 which is:

or a salt thereof.

167. The compound of any one of claims 1, 2, 6, and 10-24 wherein Z^" is: Cl^", Br^", Γ, CH3SO3^' , CF3SO3^", P-CH3C6H4 SO3^", citrate, tartrate, malate, fumarate, formate, or acetate.

168. The compound of claim 1 which is a com ound of formula (Ih):

or a salt or prodrug thereof.

169. The compound of claim 1 which is a compound of formula (Ij):

or a salt or prodrug thereof.

170. The compound of claim 1 which is a compound of formula (Ik):

or a salt or prodrug thereof.

171. The compound of claim 1 which is a compound of formula (Im):

(Im)

or a salt or prodrug thereof.

172. The compound of claim 1 which is a compound of formula (In):

or a salt or prodrug thereof.

173. The compound of claim 1 wherein:

X is N; Y is C(R²); and R³ is R^e; or

X is N; Y is C(R¹⁵); and R³ is R^c; or

X is N⁺- R¹³ (Z ); Y is C(R¹²); and R³ is R^c ; or

X is N; Y is C(R¹²); and R³ is R^e ; or

X is W-R⁵¹; Y is C(R⁵²); W is N; and R⁵¹ is absent; or

X is W-R⁵¹; Y is C(R⁵²); W is N⁺ D^"; and R⁵¹ is (d-C₆)alkyl, aryl, or aryl(C,-C₆)alkyl; or X is ^(R^XR⁸²) B^"; and Y is C(R⁸³).

174. The compound of claim 1 wherein:

X is C(R'); Y is N; and R³ is R^c or

X is C(R¹⁰) or C(R³¹); Y is N⁺-R¹⁴ ∑^'); and R³ is R^c; or

X is C(R¹⁰) or C(R³¹); Y is N; and R³ is R^c.

175. The compound of claim 1 wherein:

X is C(R¹⁶); Y is C(Rⁿ); and R³ is R^e ; or

X is C(R'); Y is C(R¹²); and R³ is R^e ; or

X is C(R³⁰); Y is C(R³¹); and R³ is R^e ; or

X is W-R⁵¹ ; Y is C(R⁵²); W is C; and R⁵¹ is hydrogen, -N⁺(R ^a)₃ D^", -C(=NR^5b)-NR^5cR^5d, -NR^e-C(=NR^5b)-NR^5cR^5d, -NR^5gR^5h, -NR^5ce-C(=NR^5cb)R^5ce, -NR^5ce-C(=0)-NR^5ccR^5cd, or (C C6)alk l that is substituted with one or more R .

176. The compound of claim 1 wherein:

X is N; Y is C(R²); and R³ is R^e; or

X is N; Y is C(R¹⁵); and R³ is R^c; or

X is N⁺- R¹³ (∑ ; Y is C(R¹²); and R³ is R^c ; or

X is N; Y is C(R¹²); and R³ is R^e .

177. The compound of claim 1 wherein:

X is C(R^!); Y is N; and R³ is R^c or

X is C(R¹⁰) or C(R³¹); Y is N⁺-R¹⁴ (Z ); and R³ is R^c; or

X is C(R¹⁰) or C(R³¹); Y is N; and R³ is R^c.

178. The compound of claim 1 wherein:

X is C(R¹⁶); Y is C(Rⁿ); and R³ is R^e ; or

X is CiR¹); Y is C(R¹²); and R³ is R^e ; or

X is C(R³⁰) Y is C(R³¹); and R³ is R^e .

179. A composition comprising a compound of formula I as described in any one of claims 1- 178, or a pharmaceutically acceptable salt or prodrug thereof, and a pharmaceutically acceptable vehicle.

180. A method for treating a bacterial infection in a mammal comprising administering to the mammal an effective amount of a compound of formula I as described in as described in any one of claims 1-178, or a pharmaceutically acceptable salt or prodrug thereof.

181. The method of claim 180 wherein the bacterial infection is a Gram -negative bacterial strain infection.

182. The method of claim 181 wherein the Gram-negative bacterial strain is selected from the group consisting of Escherchia coli, Caulobacter crescentus, Pseudomonas aeruginosa, Agrobacterium tumefaciens, Branhamella catarrhalis, Citrobacter diversus, Enterobacter aerogenes, Enterobacter cloacae, Enterobacter sakazakii, Enterobacter asburiae, Pantoea agglomerans, Klebsiella pneumoniae, Klebsiella oxytoca, Klebsiella rhinoscleromatis, Proteus mirabilis, Salmonella typhimurium, Salmonella enteriditis, Serratia marcescens, Shigella sonnet, Neisseria gonorrhoeae, Acinetobacter baumannii, Acinetobacter calcoaceticus, Acinetobacter Iwoffi, Salmonella enteriditis, Fusobacterium nucleatum, Veillonella parvula, Bacteroides forsythus, Actinobacillus actinomycetemcomitans, Aggregatibacter

actinomycetemcomitans, Porphyromonas gingivalis, Helicobacter pylori, Francisella tularensis, Yersinia pestis, Borrelia burgdorferi, Neisseria meningitidis and Haemophilus influenzae.

183. The method of claim 180 wherein the bacterial infection is a Gram -positive bacterial strain infection,

184. The method of claim 183 wherein the Gram-positive bacterial strain is selected from the group consisting of Staphylococcus aureus, Staphylococcus epidermidis, Staphylococcus saprophyticus, Streptococcus pyogenes, Streptococcus faecalis, Enterococcus faecalis,

Enterococcus faecium, Bacillus subtilis, Micrococcus luteus, Mycobacterium tuberculosis, Bacillus anthracis, Bacillus cereus, Clostridium difficile, Propionibacterium acnes,

Streptococcus mutans, Actinomyces viscosus, Actinomyces naeslundii, Streptococcus sanguis, Streptococcus pneumoniae and Streptococcus salivarius.

185. The method of claim 180 wherein the bacterial infection is a multiple drug-resistant bacterial strain infection.

186. The method of claim 185 wherein the multiple drug-resistance bacterial strain is selected from the group consisting of methicillin-resistant Staphylococcus aureus, vancomycin-resistant Enterococcus, multiple drug-resistant tuberculosis and multidrug-resistant Clostridium difficile.

187. A compound of formula I as described in any one of claims 1-178, or a pharmaceutically acceptable salt or prodrug thereof for the prophylactic or therapeutic treatment of a bacterial infection.

188. A compound of formula I as described in any one of claims 1-178, or a pharmaceutically acceptable salt or prodrug thereof for use in medical treatment.

189. The use of a compound of formula I as described in any one of claims 1-178, or a pharmaceutically acceptable salt or prodrug thereof for the preparation of a medicament for treating a bacterial infection in a mammal.