A moving condensate of para-excitons in a 3D Cu2 O crystal turns out to be spatially inhomogeneous in the direction of motion, and the registered velocities of coherent exciton packets are approximately equal to the longitudinal sound speed of the crystal. We explore a simple theoretical model to describe such properties of the Bose condensed excitons. Taking into account the exciton – phonon interaction and introducing the coherent phonon part of the moving condensate, we derive the dynamic equations for the exciton – phonon condensate. Within the Bose approximation for excitons, we discuss the conditions for the moving condensate to appear in the crystal. We calculate the condensate wave function and energy and a collective excitation spectrum in the semiclassical approximation. The stability conditions of the moving condensate are analyzed as well.