Diffusional transport across lipid membranes can be highly complex and include several parallel transport processes. It is typical for the responding lipid membrane that small changes in the membrane environment can lead to major changes in membrane structure. In a multilayer membrane, the response can lie in heterogeneous swelling and phase transformations. The changes in membrane structure profoundly affect the molecular environment and thus the local diffusion properties. This feedback mechanism generates non-linear transport behaviour where an external gradient can be used as a kind of switch to regulate the membrane barrier properties. This coupling between the dynamic and the static properties of the membrane forms the basis for this review paper that describes the basic concepts of responding membranes and illustrates some examples of where it can be applied. A major feature of responding membranes is that non-linear transport behaviour can be induced by the gradients that cause phase transformation in the membrane. This is illustrated for a lipid membrane in the presence of an osmotic gradient. The principles are also applied to the barrier of stratum corneum, the upper layer of the human skin, where it can provide an explanation for the so-called occlusion effect and the formation of the ``acidic mantle'' of the skin surface.