Acoustoelectric current saturation, which until now has only been observed in piezoelectric single crystals, is observed in thin polycrystalline zinc oxide films. Epitaxial ZnO films on c-plane sapphire and textured ZnO polycrystalline films on fused silica both exhibit current saturation phenomenon. The values of the saturation current densities are in the range 10(5)-10(6) A/cm(2), depending on the carrier concentration in the film, with corresponding saturation electric fields of 3-5 X 10(3) V/cm. In addition to the current saturation, the electrical properties of the films degraded with the onset of the acoustoelectric effect but could be restored by annealing at 250 degrees C in a vacuum for 30 min. (C) 1996 American Institute of Physics.