We investigate light wave propagation through a one-axis anisotropic medium layer with simultaneously non-unit dielectric and magnetic tensors. 4x4 - Δ▵(see manuscript ) matrix is built. We consider the general case when the dielectric and magnetic permittivity tensor elements have both positive and negative sings. We obtained the dispersion equation and then built dispersion surfaces for a homogeneous anisotropic uniaxial material when the material is negative or positive (both with respect to the wave vector and Pointing's vector orientation of the refracted wave; the sign of the material is accordingly defined below.) Electromagnetic plane waves propagating inside the medium can exhibit dispersion surfaces in the form of ellipsoids of revolution, hyperboloids of one sheet, or hyperboloids of two sheets. The conditions of negative refraction with respect to the wave vector and Pointing's vector orientation are considered. We found wave nonreciprocity for the oblique incidence on the considered system and we showed that such a system can work as an alloptical diode.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.