Catalytic efficiency of gas phase and alumina-supported bimetallic Ag_nAu_m (n + m = 2 − 4) alloy clusters is studied using density functional methods As a pre-requite, adsorption of O₂ and CO molecules, and coadsorption of both molecules on these clusters are studied in detail. O₂ and CO are co-adsorbed on nearby sites on the gas phase tetramer clusters Ag₂Au₂ and Ag₃Au. But their catalytic efficiency is hindered by large barriers (1.55 eV and 1.44 eV, respectively) to the breaking of O—O bond. Among the deposited clusters, Ag₂Au and AgAu₂ have O₂ and CO co-adsorbed on nearby locations. Of these two, Ag₂Au has a lower kinetic barrier for subsequent CO₂ formation. Thus Ag₂Au looks the most promising candidate.