XMo6HPC/Al2O3 catalysts based on Anderson-type heteropoly compounds (HPCs) with heteroatoms X = Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, and Al were synthesized. The catalytic properties of the prepared samples were studied in naphthalene hydrogenation, dibenzothiophene hydrodesulfurization, and quinoline hydrodenitrogenation. The highest activity was exhibited by the catalysts with X = Co and Ni; the lowest, with X = Cu. It was found that dibenzothiophene hydrodesulfurization and naphthalene hydrogenation occur on different active sites, whereas the sites of the hydrogenation of naphthalene and dibenzothiophene have a similar nature. Quinoline (at a nitrogen content of 100 ppm) had a different effect on the catalytic properties: it inhibited the hydrogenation of dibenzothiophene and naphthalene, but promoted the desulfurization of dibenzothiophene.