Density functional theory calculations within the generalized gradient approximation have been performed for the interaction of oxygen with reduced SnO2 and Ti/SnO2 (110) surfaces. We found small dissociation energies for a peroxo species on both surfaces and slightly lower migration barriers of similar to6-13 kcal/mol for an oxygen atom produced by the dissociation of O-2 on the Ti/SnO2 surface compared to migration barriers of similar to13-18 kcal/mol on the SnO2 surface. An analysis of the electronic density of states indicates that an adsorbed oxygen atom coupled with the nearest neighboring bridging oxygen vacant site should be an O- species with catalytic activity on the surfaces. The maximum concentration of O-species on the perfectly reduced SnO2 surface is half the concentration of the vacant bridging oxygen sites, which favors yielding a higher concentration of O- compared to the reduced Ti/SnO2 surface. The limited migration of the O- species on the reduced Ti/SnO2 surface may be an advantage for controlling the catalytic activity. The theoretical reaction rates for the dissociation, recombination, and desorption of adsorbed oxygen species on the surfaces have been discussed using transition-state theory.