Measurements of current-voltage characteristics for ZnO single crystals at temperatures between 77 and 640 °K are reported. Because of the buildup of an intense acoustic flux, a strong current saturation sets in when the trap-controlled electron drift velocity is equal to the velocity of sound. The temperature dependence of the saturated current is discussed in terms of a trapping model which includes nonlinear trapping effects. Our results indicate the presence of a shallow-donor level with an ionization energy of 50 meV and a deep-donor level approximately 230 meV below the conduction-band edge. The capture cross section for the shallow donors is determined to be about 5 × 10-12 cm2 at 100 °K.