Direct synthesis of H2O2 from H-2 and O-2 is a reaction of commercial interest. In addition, this reaction is likely to occur in situ during gas-phase propylene epoxidation using H-2 and O-2 on Au/Ti-based catalysts. To consider the effect of alloying on H2O2 formation on Au-containing clusters, we have performed a B3LYP-based density functional theory analysis of H2O2 formation from H-2 and O-2 on Ag, Ag-Au, Cu, Cu-Au, Pd, and Pd-Au dimers and trimers. The LANL2DZ pseudopotential and the corresponding double-zeta basis set was used for heavy atoms, while a 6-311+G(3df) basis set was used for O and H. We report kinetic and thermodynamic parameters at standard conditions (298.15 K, 1 atm) for following elementary steps: (1) molecular adsorption of O-2, (2) first H-2 addition to make the hydroperoxy (OOH) species, and (3) second H-2 addition to make H2O2. Formation of the OOH species is thermodynamically (and in some cases kinetically) unfavorable on all the Cu- and Ag-containing dimers. Although the kinetics is favorable, formation of the OOH species is thermodynamically unfavorable on all the Cu- and Ag-containing trimers except CuAu2. The H2O2 formation step is, however, thermodynamically unfavorable on CuAu2. Contradictory to findings on pure Au clusters, we predict that the H2O2 formation on small Ag, Ag-Au, Cu, and Cu-Au clusters is not feasible mainly due to the unfavorable thermodynamics (298.15 K, 1 atm) of the H-2 addition steps. These predictions are also applicable to Pd-2, Pd2Au, and PdAu2 clusters. On the other hand, formation of the OOH and H2O2 species is both kinetically and thermodynamically favorable on PdAu and Pd-3 clusters. Thus, on the basis of computational screening of the catalytic activity of fifteen pure and Au-alloy dimers and trimers reported here, in addition to Au-3, we identify PdAu and Pd-3 as potentially active clusters for OOH and H2O2 formation from H-2 and O-2.