The dispersion properties of transverse electric nonlinear waves in a three-layer slab waveguide which consists of a double negative material (DNM) guiding layer sandwiched between an intensity-dependent refractive index substrate and semi-infinite linear dielectric cover are investigated. The dispersion properties for self-focusing and self-defocusing substrate nonlinearity are presented. The effects of the negative parameters of the DNM on the dispersion characteristics are investigated
