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Electromagnetic waves guided by the interface between two nonlinear media, and a nonlinear and a linear medium are investigated theoretically and numerically. Both s‐ and p‐polarized waves are analyzed and the guided wave power versus guided wave vector is evaluated for a variety of material conditions. The consequences of two different versions of the uniaxial approximation for the p‐polarized case are compared. The power‐dependent attenuation is approximately evaluated.