The study of the oxygen exchange of mixed ionic electronic conducting oxides with the gas phase, which determines the efficiency of devices planned to be used in distributed power generation and industrial chemistry is complicated by the strong dependence of their properties on widely varying oxygen nonstoichiometry delta. A new fruitful approach, in which non-stoichiometric oxides are considered as continuous delta-homologous series proposed for solving this problem, requires the development of a new methodology for the collection and analysis of the kinetic data. La0.6Sr0.4CoO3-delta (LSC64) delta-homologues were used as examples to demonstrate the novel methodology for studying the kinetics of oxygen exchange by oxygen partial pressure relaxation technique. It includes analysis of the kinetic data in the isostoichiometric cross-section, a non-linear model of relaxation kinetics, a detailed consideration of the mass balance in the reactor, accounting for the particle size distribution in the sample and the response time of the experimental setup. For the continuous series of LSC64 delta-homologues, the Bronsted-Evans-Polanyi relationship is established: the linear correlation of the Gibbs activation energy with the chemical potential of the oxide, as well as the compensation effect between the activation parameters of the equilibrium oxygen exchange rate.