The dissociation dynamics of oxygen on silver surfaces is studied theoretically. The method is based on a quantum-mechanical time-dependent non-adiabatic picture. A universal functional form for the potential energy surfaces is employed. The diabatic potentials describing the sequence of events leading to dissociation begin from the physisorption potential crossing over to a charged molecular chemisorption potential and crossing over again to the dissociated atomic-surface potential. Within such a potential surface topology, two different surfaces leading to dissociation are studied: the empirical potential of Spruit and the ab-initio potential of Nakatsuji. It is found that the system is captured by the molecular chemisorption well for a considerable length of time, long enough for thermalization. Thus the calculation is split into two parts: the calculation of “direct” dissociation probability and the calculation of nonadiabatic dissociative tunneling rate from the thermalized chemisorbed molecular state. For the direct probabilities, the Fourier method with the Chebychev polynomial expansion of the evolution operator is used to solve the time-dependent Schrödinger equation. For the tunneling rate calculation, a similar expansion of Green's operator is used. The output of the direct-reaction calculation is the dissociation probability as a function of the initial energy content, while the tunneling calculation yields the dissociation rate. The dependence of the direct dissociation probability on the initial kinetic energy is found to be non-monotonic. A strong isotope effect has been found, favoring the dissociation of the light species.