Approximate boundary conditions in the first and second approximations are obtained for stratified tensor media. The approximate conditions make possible the solution of electrodynamic problems without examination of the fields inside the anisotropic layers. The layer thickness in all cases is assumed to be small compared with the wavelength in any layer. The accuracy of the approximate boundary conditions is estimated for one particular example. It is shown that boundary value problems involving ferrite layers near the waveguide walls reduce to solutions of eigenvalue problems with definite boundary conditions along the periphery.