Using the general methods of non-equilibrium thermodynamics, a theory for anisotropic polarizable media in which dielectric relaxation phenomena occur is developed. Assuming that ii microscopic phenomena give rise to dielectric relaxation, the contributions of these phenomena to the macroscopic polarization are introduced as vectorial internal degrees of freedom in the Gibbs relation. Moreover, it is assumed that a viscous flow phenomenon occurs which is analogous to the viscous flow of ordinary fluids. The phenomenological equations connected with irreversible changes in the polarization and the generalized laws of Ohm, Fourier and Newton are derived, and the Onsager-Casimir reciprocity relations are formulated. For the case that the equations of state can be linearized explicit expressions for the free energy, the internal energy and the entropy are given and it is shown that a complete set of equations describing the mechanical, electromagnetic and thermodynamic behaviour of the media studied in the present paper can be obtained.