  We analyze nonlinear guided waves in a planar waveguide made of a left-handed
material surrounded by a Kerr-like nonlinear dielectric. We predict that such a
waveguide can support fast and slow symmetric and antisymmetric nonlinear
modes. We study the symmetry breaking bifurcation and asymmetric modes in such
a symmetric structure. We analyze nonlinear dispersion properties of the guided
waves, and show that the modes can be both forward and backward.
