Properties of TE waves in a slab waveguide composed of five layers, including two Kerr-like nonlinear layers, are analyzed and examined. We find in particular the occurrence of an asymmetric mode, in addition to the expected symmetric and antisymmetric modes, though the waveguide geometry is symmetric. For the TE0symmetric mode, TE1antisymmetric and asymmetric modes, the dispersion curves, the relations between the effective index and the optical power density, and the variations of the transverse electric field patterns are illustrated and discussed in detail. As a result of this analysis, the regions in which the respective modes mainly reside are elucidated. We find that the effective index value of the symmetric mode at which the guide power vanishes is larger than that of the antisymmetric mode. For the case in which the effective indexes of the asymmetric and antisymmetric modes are identical, the power in the former mode is found to be larger than that in the latter.