Ternary metal-oxide interfaces adopt in each point of their T-mu(O2) thermodynamical stability range a different interfacial equilibrium chemistry. While for reactive and partially reactive interfaces, changes in the oxygen chemical potential may induce the formation of new product phases for nonreactive interfaces, only the local interfacial chemistry is changed through Gibbs' adsorption/desorption of interfacial oxygen or oxide metal. This is demonstrated by experimental ELNES studies for gamma-alumina-copper interfaces, which show large oxygen excess at high oxygen activity and stoichiometric composition in an intermediate oxygen activity range. A model of interfacial point defects recently developed by the author is used to evaluate changes in the interfacial chemistry as function of the oxygen chemical potential for the studied interface. In electrochemical cells, interfacial compositions at metal electrode-oxide electrolyte are strongly modified by the applied electrical potential. The modifications under applied potential in current-free state and under current flow are discussed.