Supports based on pseudoboehmite, ultrastable zeolite Y, and ZSM-5 with different silica ratio and concentration of acid sites are prepared. NiMoS catalysts are synthesized by the incipient wetness impregnation of the prepared supports by the joint solution of H3PMo12O40 and nickel citrate. The composition and properties of the supports and catalysts are studied by low-temperature nitrogen adsorption, ammonia temperature-programmed desorption, IR spectroscopy of pyridine adsorption, and high-resolution transmission electron microscopy. Catalytic properties are investigated in dibenzothiophene hydrodesulfurization (HDS), naphthalene hydrogenation (HYD), and hexadecane hydrocracking (HC) concurrent reactions in a flow unit equipped with a microreactor. It is shown that the HDS activity of the synthesized samples declines as the dispersity of active-phase particles decreases in correlation with a change in the surface area of support mesopores. It is shown that the NiMo/ZSM-5/23 catalyst exhibits a high activity in naphthalene HYD and subsequent reactions of tetralin and decalin naphthene ring opening and hexadecane HC. It is found that the activity of zeolite-containing catalysts in naphthalene HYD grows with the proportion of BrOnsted acid sites.