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Dispersion equations are proposed for acoustoelectric Rayleigh waves in a periodically layered piezoelectric half space with various types of boundary conditions. The properties of the medium are specified by the determining relations for the 6mm crystallographic class. These equations are obtained using the mathematical formalism of periodic hamiltonian systems. This approach makes it possible to include the anisotropy and the piezoelectric interaction of the mechanical and electric fields and is valid for stratified media with arbitrary variations in the properties along the periodicity axis. Numerical results are presented for alternating layers of CdS and ZnO. The influence of the piezoelectric effect and type of boundary conditions on the dispersion spectra of surface waves is examined.