In materials, which are exposed to thermodynamic potential gradients, i.e., gradients of chemical potentials, electrical potential, temperature, or pressure, transport processes of the mobile components occur. These transport processes and the coupling between different processes are not only of fundamental interest, but are also the origin of degradation processes, such as kinetic demixing and decomposition and changes in the morphology of the material, all of which are of great practical relevance. Two classes of materials will be considered, semi- and ion conducting oxides and ion conducting halides. In oxides, kinetic demixing of the cations in a multicomponent oxide and kinetic decomposition of the oxide under the influence of an applied thermodynamic potential gradient will be considered for homovalent oxide solid solutions and for heterovalently doped oxides. In ion conducting halides, the morphological stability of solid/solid interfaces, which are driven by an external electrical potential gradient, is studied. Monte Carlo simulations show that the morphological stability of the interface is determined by the difference in the ionic conductivities of the two crystals. (C) 2003 Elsevier Science Ltd. All rights reserved.