A new approach for developing fundamental equations of oxygen permeation through thin mixed-conducting oxide ceramic is presented considering both surface reactions on membrane-gas interfaces and the diffusion of charged species in the bulk oxide. The essence of this work is the coupling of surface reactions with the bulk diffusion using a novel approach which differs from the conventional Wagner theory applicable only to limited cases. With this approach, fundamental equations based on various permeation mechanisms can be derived for oxygen permeation through thin mixed-conducting oxide membranes, which is impossible using conventional approach. In general, the final results are a complex implicit equation correlating the oxygen permeation flux to the driving force, membrane thickness, and rate constants with physical significance in each step. Somewhat simpler theoretical oxygen permeation equations are obtained for some special cases (mixed-conducting membranes with a rate-limiting step, ionic-conducting membranes, ionic-conducting membranes with a reducing agent in permeate side). Theoretical results derived using this new approach agree excellently with the experimental oxygen permeation data. It is theoretically and experimentally shown that for ionic conductors, the surface permeation parameter measured by the dynamic permeation method is directly related to the oxygen isotope exchange rate constant measured under equilibrium conditions.