The membrane with continuously varying and pressure-dependent local permeability P may show a dependence of transport property for gases and vapors on the direction of flow. Such an asymmetry occurs only if the deviation of local permeability from ideality varies from layer to layer. In mathematical formulation, this means that the local permeability is an irreducible function of location and pressure, i.e., not a product of a function of location and a function of pressure. The membrane permeability is higher if the side with greater deviation from ideal, i.e., constant permeability, is exposed to the higher pressure. For two simple cases the currents in both directions and their ratio at constant pressure difference were calculated. It turns out that the asymmetry of permeability increases with increasing deviation from ideality up to a maximum, after which the membrane tends to return to symmetry. An additional result of this investigation is the conclusion that Fick's law, i.e., the proportionality of the diffusion current to the negative concentration gradient is inapplicable not only to inhomogeneous membranes but also to homogeneous not ideal membranes.