A new presentation of tensors of relative phase permeabilities for anisotropic porous media is considered.The relation between the tensors of absolute and phase permeabilities is postulated to be represented by a tensor of 4th rank. It is shown that in this case the relative phase permeabilities depend not only on the saturation, but also on the ratios of main values of an absolute permeability tensor. The obtained relations for phase permeabilities are used for analyzing the results of numerical modeling of two-phase flow in the orthotropic porous medium. The versions of complex studies for obtaining phase permeabilities in anisotropic porous media from the results of laboratory measurements are discussed.