We consider a cylindrical nematic liquid crystal waveguide with an infinite homogeneous isotropic cladding, and study the propagation of TM and TE modes. The dielectric tensor of the liquid crystal core which governs wave propagation is determined by the configuration of the nematic director. For TM modes, propagating optical fields alter the director configuration, and thus change the dielectric tensor. For both TM and TE modes, we consider the effects of the propagating fields on the order parameter tensor. We use an iterative numerical scheme to determine the propagation constant as a function of optical power. For the TM modes, the propagation constant increases continuously with the power. For the TE modes, an abrupt increase is found.