To generate improved catalytic capacity, especially, selectivity in disproportionation reaction and/or transalkylation reaction of an alkyl aromatic hydrocarbon.

This composite catalyst contains at least one mordenite structure type zeolite, pref., mordenite being at least partially, pref., substantially entirely in an acid form, at least one mazzite structure type zeolite, pref., omega zeolite at least partially, pref., substantially entirely being in a acid form and at least one matrix (or a binder) and also contains at least one element selected from metals of groups IB, VIII according to circumstances. This catalyst is used in the disproportionation and/or transalkylation of toluene and/or an aromatic compd. containing at least 9 carbon atoms.