The oxidation of small silver clusters (Ag-n, n <= 9) was investigated through electronic structure calculations based on density functional theory. The adsorption energies of molecular and dissociated adsorption show a pronounced odd/even alternation, with lower energies calculated for even-sized clusters. Molecular adsorption is favored for n <= 5, whereas dissociation is preferred for the larger sizes. Molecular oxygen is adsorbed in atop (Ag, Ag-2, Ag-6, Ag-8) or bridge (Ag-3, Ag-4, Ag-5, Ag-7, Ag-9) configurations, and atomic oxygen is preferably adsorbed in 3-fold hollow positions. Results for stoichiometric (Ag2nOn) clusters were compared to O-2 adsorption on Ag(111), and ab initio thermodynamics was used to estimate the temperature for the oxide-to-metal phase transition. The barrier for O-2 dissociation on Ag-8 was calculated to be higher than the corresponding barrier on Ag(111), which indicates a slower oxidation process. Adsorption of NOx onto the oxidized clusters was found to proceed through a formal reduction of the clusters; that is, NOx is adsorbed as NOx+1 with x = 1, 2.