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The dispersion relations for TE polarized waves guided by thin dielectric (planar integrated optics) films, surrounded on one or both sides by media with intensity-dependent refractive indexes, are solved numerically and interpreted. Comparisons are made between these nonlinear guided waves and the usual integrated optics modes associated with linear media. For media characterized by self-defocusing nonlinearities, increasing guided wave power leads to a decrease in the guided wave effective index and to mode cutoffs characterized either by finite or diverging total guided wave powers. For self-focusing media, the effective index increases with increasing power. New wave solutions are obtained with power thresholds and anomalous power-dependent field distributions. These characteristics are illustrated by numerical calculations for a specific material system and possible applications to optical devices are discussed.