We study the acoustoelectric effect generated by surface acoustic waves (SAW) in a high-mobility two-dimensional electron gas with isotropic and especially small-angle impurity scattering. In both cases the acoustoelectric effect exhibits Weiss oscillations periodic in B–1 due to the commensurability of the SAW period with the size of the cyclotron orbit and resonances at the SAW frequency =kc multiple of the cyclotron frequency. We describe how oscillations in the acoustoelectric effect are damped in low fields where c*1 (with the time scale * dependent on the type of scattering) and find its nonoscillatory part, which remains finite to the lowest fields.