To reveal the reason of asymmetry of the diffusion permeability of bi-layer electrodialysis membranes the following problems have been solved using the model of "homogeneous porous membrane": - diffusion of non-electrolyte solutions across a bi-layer membrane; - diffusion of electrolyte solutions across a non-charged bi-layer membrane; - diffusion of electrolyte solutions across a charged single layer membrane; - diffusion of electrolyte solutions across a charged bi-layer membrane. It is shown that the main factor responsible for the asymmetry is the difference between absolute values of densities of fixed charges (or so called "exchange capacities") of different layers of a membrane under investigation. Only in this case the ratio of the thickness of the membrane layers as well as the ratio of ion diffusivities contributes also to the asymmetry of the diffusion permeability. In the present review we survey and generalize our previous investigations and propose a new theory of asymmetry of diffusion permeability of bi-layer membranes. We have deduced explicit algebraic formulas for the degree of asymmetry of diffusion permeability of bi-layer membranes under consideration.