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We present a theoretical model to study the effect of microwave radiation on Weiss oscillations. In our proposal Weiss oscillations, produced by a spatial periodic potential, are modulated by microwave radiation due to an interference effect between both, space and time-dependent, potentials. The final magnetoresistance depends mainly on the spatial period of the spatial potential and the frequency of radiation. Depending on the values of these parameters, we predict that Weiss oscillations can reach zero resistance states. On the other hand, these dissipationless transport states, created just by radiation, can be destroyed by the presence of a space-dependent potential.