A phenomenological model for the spreading of nematic liquid crystals on fibers of circular cross section is presented. The model is used to calculate the wetting thresholds of nematics on fibers for three characteristic director orientations: axial (undistorted), radial (splay), and azimuthal (bend); the wetting thresholds are given in terms of critical film thickness h(c) and critical spreading parameter S-c. When the spreading parameter S is greater than the critical value S-c, nematic liquid crystal fiber wetting is similar to that of viscous fluids when director distortions are absent. In other cases when nematic liquid crystals spread on fibers the distortion due to the cylindrical geometry gives rise to Frank elasticity, For symmetric director boundary conditions the characteristic modes of splay and bend increase the magnitude of critical spreading parameter S-c. It is found that when spreading occurs (S > S-c) the equilibrium film thickness decreases with increasing elastic storage. The film thickness for rod-like and disc-like nematics differs because the splay-bend elastic anisotropy is reversed.