A composite waveguide structure, which is a crystal with a diffusion mechanism for the formation of a nonlinear photorefractive response, the surface of which is coated with a non-linear Kerr defocusing type, is considered. It is shown that there exist TM polarized nonlinear surface waves of two types, which differ in the range of existence and the profile of field decay. The propagation modes of nonlinear surface waves are determined in which the field intensity can be maximum or minimum near the surface or at the boundary of the coated crystal.