To obtain a defect-free nonwoven web of the subject microfibers by melt spinning a blend of a polyarylene sulfide and a specific organic phosphite or phosphonite additive while preventing the polymer from oxidation.

This microfiber web is obtained by extruding, into a high-speed air jet, from a plurality of orifices, a blend of (A) a polyarylene sulfide (pref. polyphenylene sulfide) and (B) an organic phosphite or phosphonite additive of formula I, II, III (R1 to R4 are each an alkyl, aryl, alkoxy or the like; and X is an alkylene, arylene or the like) or formula IV (R5 is t-butyl, phenyl or the like; and one of R6 and R7 is H, the other being methyl, t-butyl or the like) at a temperature higher than the melting point of the component A and collecting the resultant microfibers in a filamentous state; wherein the amount of the component B to be added prior to the blending is about 0.1-about 5 wt.%. The method as described above is effective for preventing production of spitters and shots as impurities or defects.