Description of mass transport in a media or through a membrane usually is based on the assumption that a standard chemical potential go of a substance is constant and does not change with the distance in the media or membrane. This common assumption is not valid for asymmetrical or nonhomogeneous membranes. More accurate analysis of the transport, given in this paper, is based on one of the major principles of linear thermodynamics, according to which any flux is proportional to the gradient of electrochemical potential mu. It also takes care of possible changes of standard chemical potential go in asymmetrical media or membrane. It is demonstrated that an asymmetrical media, but not a membrane separating two similar phases, can act as a diffusion-based diode. Still, even with the membranes, if both the standard chemical potential and activity gradients are negative, the flux is increased and the time lag is decreased. Time lag, which is usually used to calculate a diffusion coefficient, can be much less than the one on the basis of the Einstein-Barrer equation. Asymmetry also allows additional improvement of membrane selectivity. Transport through both the membrane interface and the inner part of asymmetrical membrane far from equilibrium even for nonelectrolytes can be described by equivalent circuit, which has three diodes, with one of them looking to the opposite direction. The developed model and equivalent circuit are reduced to the common concepts if the asymmetry of the membrane decreases.