The dispersion properties of guided waves in an anisotropic film sandwiched between a left-handedmaterial (LHM) and a dielectric are investigated in this work. Detailed mathematical derivationof the dispersion relation is presented. Both the anisotropic guiding layer and the LHM are assumedto be dispersive. Many interesting features have been found. The dispersion properties exhibita slight dependence on the parameters of the anisotropic guiding layer whereas they showa significant change with any perturbation in some of the LHM layer parameters, especially forω>5.2GHz.The dispersion properties of guided waves in an anisotropic film sandwiched between a left-handedmaterial (LHM) and a dielectric are investigated in this work. Detailed mathematical derivationof the dispersion relation is presented. Both the anisotropic guiding layer and the LHM are assumedto be dispersive. Many interesting features have been found. The dispersion properties exhibita slight dependence on the parameters of the anisotropic guiding layer whereas they showa significant change with any perturbation in some of the LHM layer parameters, especially forω>5.2GHz