The current oscillations which are observed in piezoelectric semiconductors, such as cadmium sulfide, are often accompanied by a high field domain which moves through the sample at the velocity of sound. These domains may be a result of the negative differential conductivity which is produced in the material by a large component of acoustoelectric field. This field opposes the applied field when the drift velocity exceeds the velocity of sound. We determine from the linear theory a threshold condition for the onset of the negative differential conductivity and show that this model is in agreement with the experimental observations reported here on CdS and elsewhere on GaAs.