The reactivity of diselenides and ditellurides of general formula (RX)2 (X = Se, Te; R = H, CH3, Ph) toward hydrogen peroxide was studied through a computational approach based on accurate Density Functional Theory (DFT) calculations. The aliphatic and aromatic dichalcogenides have been chosen in light of their activity in glutathione peroxidase (GPx)-like catalytic cycles and their promising features as efficient antioxidant compounds. The reaction products, the energetics and the mechanistic details of these oxidations are discussed. Analogous disulfides are included in our analysis for completeness. We find that the barrier for oxidation of dichalcogenides decreases from disulfides to diselenides to ditellurides. On the other hand, variation of the substituents at the chalcogen nucleus has relatively little effect on the reactivity.