The propagation characteristics of nonlinear waves guided by a metal film that is bounded on one or both sides by media characterized by an intensity‐dependent refractive index are discussed. The dispersion relations are solved numerically for both self‐focusing and self‐defocusing media with nonlinearities typical of InSb at a wavelength of 5.5 &mgr;m. In particular, the power dependence of the guided wave wave vector, of the field distributions, and of the wave attenuation are obtained for the multiple wave solutions allowed by the dispersion relations. In the appendix we evaluate the power dependence of the attenuation ofs‐polarized surface‐plasmon polaritons guided by a metal film.