The oxirene is an unsaturated heterocyclic molecule with one oxygen atom and two carbon atoms. Its hydrogenation has been performed on two catalytic site based on molybdenum disulfide (MoS₂) and tungsten disulfide (WS₂) of MoS₃H₃⁺ and WS₃H₃⁺ type, respectively. The calculations were carried out using the SCF and MP2 methods and B3LYP functional calculations. The results obtained showed that the hydrogenation of the oxirene is possible on these two kinds of catalytic sites on the one hand, and the reaction product is the acetaldehyde molecule, on the other hand. The reaction process study that led to the results showed that the catalytic hydrogenation of the oxirene is a dissociative process. On the basis of the variation of some parameters during the process, a mechanism of the reaction has been proposed.