Permeation through the membrane with different surface conditions on the inlet and outlet sides is analyzed. Two regime parameters characterizing the rates of processes on two sides of the membrane with respect to the rate of bulk diffusion are introduced. These regime parameters determine the concentration profile and the permeation rate. General equations for the concentration and the permeation flux are obtained. Three basic limit regimes are considered as partial limit cases of the general equations. These are diffusion limited regime (DLR), outlet surface limited regime (OLR), and inlet surface limited regime (ILR). The latter has two modes with qualitatively different concentration profiles. Boundaries between the regimes and approximation formulas for the permeation rates in these regimes have been found. Features of permeation in the limit cases and in intermediate regions are analyzed. (C) 2009 Elsevier B.V. All rights reserved.