The mechanism of activation of a hydrogen molecule upon interaction with the surface of nanosized particles of the MoS2 hydroconversion catalyst has been modeled using a quantum-chemical method of the density functional theory (DFT) with the hybrid functional B3LYP/dgdzvp in the cluster approximation. Two clusters, Mo2S4 and Mo3S6, have been considered as structural models of nanosized catalyst particles. It has been shown that the primary event of interaction of molecular H-2 with the catalyst surface is the chemisorption of hydrogen atoms on the molybdenum atom with H-H bond breaking. The local minima of the total electronic energy of the complexes in the chemisorption of hydrogen atoms on Mo and S atoms and the energy of the transition state between local minima have been found. It has been established that the stability of the complexes [Mo(3)S(6)aEuro broken vertical bar H-2] varies in the order: [center dot center dot center dot MoH2] > [(S)H center dot center dot center dot(S)H] > [(Mo)H center dot center dot center dot(S)H] > [(Mo)H center dot center dot center dot(Mo)H] > [center dot center dot center dot SH2].