The propagation behavior of the four lower-order modes, HE11, TEol, TMol, and HE21, in a radially anisotropic cylindrical waveguide with liquid crystal cladding is studied both theoretically and experimentally. The cylindrical waveguide is a doubly-clad fiber with an isotropic core and inner cladding and a radially anisotropic outer cladding made of nematic liquid crystal. Theoretically, the propagation and decay constants for the TEol and TMol modes are obtained by solving the wave equations exactly, while those for the HEll and HEzl modes are derived using perturbation techniques under the weakly guiding approximation. It is predicted that in such a structure the guided TEol mode can be separated from the leaky HEII, TMoI, and HEzr modes. The theoretical results show good agreement with the experimental observations for a 3 em long fiber cell with a 5 pm inner cladding radius.