The propagation of acoustoelectric waves in uniform cylinders was investigated in [2-8, ii, 12]. Solutions of mainly one-dimensional problems have been obtained for nonuniform piezoactive waveguides [9, 13]. Papers [I, I0], which provide analyses of the dispersion relationships for a plane layer, constitute an exception. We shall consider here the propagation of acoustoelectric waves in a circular cylinder consisting of a finite number of piezoceramic layers. Consider a circular cylinder with the outside radius rQ and the inside radius r0 (rQ r0 = H is the cylinder thickness), consisting of a finite number Q of piezoceramic layers, which are polarized in different directions (axial, radial, or circular). The equations of motion of a continuous, elastic medium, together with the equations of induced electrostatics of dielectrics and the Cauchy and piezoelectric effect relationships, constitute a closed system of equations describing the elastic and electromagnetic processes in the piezoelectric medium. In the cylindrical coordinate system r, 8, z these relationships have the following form: