The adsorption of H2O2 on Pt and Pt- M alloys, where M is Cr, Co, or Ni, is investigated using density functional theory. Binding energies calculated with a hybrid DFT functional (B3PW91) are in the range of -0.71 to -0.88 eV for H2O2 adsorbed with one of the oxygen atoms on top Pt positions of Pt-3, Pt2M, and PtM2, and enhanced values in the range of -0.81 to -1.09 eV are found on top Ni and Co sites of the Pt2M clusters. Adsorption on top sites of Pt-10 yields a weaker binding of -0.48 eV, whereas on periodic Pt(111) and Pt3Co(111) surfaces, H2O2 generally dissociates into two OH radicals. On the other hand, attempts to attach H2O2 on bridge sites cause spontaneous dissociation of H2O2 into two adsorbed OH radicals, suggesting that stable adsorptions on bridge sites are not possible for any of the clusters or extended surfaces that are being studied. We also found that the water-H2O2 interaction reduces the strength of the adsorption of H2O2 on these clusters and surfaces.