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We present a theoretical proposal to study the effect of microwave radiation on Weiss oscillations. We present a novel theoretical alternative to treat Weiss oscillations based on the effect that a unidirectional spatial periodic potential, i.e., a superlattice, produces on the scattering conditions of a two-dimensional electron system. In our proposal Weiss oscillations are modulated by microwave radiation due to an interference effect between both, spatial and time-dependent, periodic potentials. The final profile presented by the magnetoresistance depends mainly on the spatial period of the superlattice and the frequency of radiation. Depending on the values of these parameters, we predict that Weiss oscillations can reach dissipationless transport states.