In this paper, basing on the anisotropic properties of longitudinal inhomogeneous nondepolarizing media with linear phase anisotropy, more general type of media with elliptical phase anisotropy was studied. The features of propagation of light with privileged states of polarization were observed. Transformation of polarization states of eigenwaves along z axes of light propagation was studied. The orthogonalization properties inherent to this type of medium were obtained. Evolution of linear polarized light in this media was presented and discussed.