The theory of acceleration waves is applied in the analysis of the formation and propagation of acoustoelectric domains in piezoelectric semiconductors. A one‐dimensional version of the general nonlinear electroelastic equations for deformable semiconductors recently presented is employed in the analysis. Consequently, the mechanical and dielectric nonlinearities are included in the analysis as well as the semiconduction nonlinearity. Equations are derived for both the propagation velocity and the amplitude of the growing disturbance as a function of the state of the material immediately ahead of the wave front. These rather general results are specialized to the case of a homogeneous steady state ahead of the wave and the condition for the threshold field is determined. In this latter case the wave front propagates with constant velocity and the amplitude equation indicates the formation of a shock in a finite time for conditions conductive to domain formation. When the electrical conduction equation, which can be quite general in this treatment, is specialized to the form usually employed for semiconductors, the aforementioned more general condition for the threshold field reduces to the known result.