The hydrogenation of naphthalene, toluene, and 2-methylnaphthalene used as model compounds; the hydrodearomatization of the methylnaphthalene fraction; and the hydrocracking of oil sludge over Ni-W sulfide catalysts supported on BEA/TUD, BEA/SBA-15, and ZSM-5/SBA-15 composites containing SBA-15 and TUD mesoporous silicates have been studied. Catalytic tests have been conducted in an autoclave at 300-400 degrees C and an initial hydrogen pressure of 50-90 atm. It has been found that the highest activity is exhibited by the catalyst based on the ZSM-5/SBA-15 (1) composite prepared by the double-templating synthesis and characterized by a specific surface area of 400 m(2)/g and an acidity of 409 mu mol/g. Thus, in the case of dearomatization of the methylnaphthalene fraction at 300 degrees C and an H-2 pressure of 50 atm, the content of diaromatic compounds has decreased from 99.0 to 53.4%, while the amount of sulfur compounds has decreased almost 15-fold. The hydrocracking of oil sludge over NiW/ZSM-5/SBA-15 (2) at 400 degrees C and an H-2 pressure of 90 atm has led to an increase in the content of light fractions to 52%.