The transfer of matter and charge across interfaces between two solids is generally related to processes of defect relaxation in the regions near the interface. A transfer rate which exceeds the rate of defect relaxation may lead to degradation of the interface, causing a feedback effect for the transfer itself. As a consequence, non-linear phenomena (dissipative structures) like periodic oscillations of the interfacial properties can occur under conditions far from equilibrium. Experimental examples are discussed.