Guided waves with unique, power-dependent properties arise when one or more of the media bounding a guiding film exhibits an intensity-dependent refractive index. Previous theoretical work on this problem has been based formalism-limited to Kerr-type nonlinear media in which the change in refractive index is quadratic in the optical field. In this paper, a formalism recently reported by Langbein et al. is used to investigate nonlinear guided wave solutions in more realistic material systems. It is shown numerically that saturation of the optically induced change in the refractive index can dramatically alter, and in some cases eliminate, the more interesting power-dependent features of the solutions. Nonlinear wave solutions are also investigated for a larger class of media characterized by refractive indexes which depend on the optical field raised to some arbitrary power.