The propagation of guided electromagnetic waves in liquid crystal slab waveguides is considered. The dielectric properties of the liquid crystal layer which govern wave propagation are determined by the configuration of the nematic director. We examine TE and TM modes of a slab dielectric waveguide consisting of a liquid crystal layer which is both anisotropic and inhomogeneous. The uncoupled wave equations for these modes are derived; the equation describing the TM modes is complex. We show that a real propagation constant β exists for all frequencies above cutoff, and obtain the complex field distribution by solving the wave equation using an effective novel numerical technique.