Hydrocracking reactions of diphenylmethane and tetralin were carried out over three kinds of zeolites with or without NiW sulfide to discuss the roles of catalytic bifunctionality in two types of hydrocracking reactions. It was found that strong acid sites were not needed for the hydrocracking of diphenylmethane, while the conversion of tetralin required relatively strong acid sites. Ultra-stable Y zeolite with strong acidity exhibited high hydrocracking activity for both reactions. In contrast, mordenite catalysts did not show high activity for either hydrocracking, though, isomerization of tetralin and excess hydrocracking to gaseous products proceeded. The superior performances of ultra-stable Y zeolite in the tetralin hydrocracking were suggested to be related to the hydrogen transfer ability. In most cases, the loading of NiW sulfide enhanced catalytic activity. In the diphenylmethane hydrocracking, the role of NiW sulfide was found to supply active hydrogen to the hydrocracking active sites on zeolite and to prevent polymerization of benzyl cations. In the tetralin hydrocracking, the dehydrogenated products from tetralin were rehydrogenated over NiW sulfide.