Theoretical impedance relationships in a limiting process with non-steady-state surface diffusion were derived based on the interfacial conductivity concept at the interface between an oxygen ion conductor and a metallic electrode. While the non-steady-state surface diffusion of adsorbed neutral oxygen on the metallic electrode could be described by Fick's second law, approximated and equivalent equations to the Warburg impedance and Gerischer impedance were derived according to the boundary conditions and occurrence of dissipation by the chemical reaction. The diffusion related to the electrochemical impedance signal is not the diffusion of the oxygen ions. In addition, it is not necessary to assume an electrochemical potential gradient or profile of the free electrons in the metallic electrode. The relationships obtained in this paper indicate that electrochemical potential measured by an instrument is clearly defined by the electrochemical potential of free electrons at the triple phase boundary. The meaning of the equivalent electrical circuits corresponding to the impedance spectra is reconsidered from the view points of the interfacial conductivity concept. Crown Copyright (C) 2013 Published by Elsevier B.V. All rights reserved.