Perovskite related oxides ABO_3−δ exhibiting mixed ionic–electronic conductivity (MIEC) possess large deviations from the oxygen stoichiometry. When providing excellent application potential, this feature also makes it very difficult to study the reaction mechanism between such oxides and molecular oxygen, also known as the oxygen reduction reaction. The complexity of the theoretical interpretation of kinetic experiments originates from the significant dependence of the kinetic and equilibrium properties of MIEC oxides on δ. It is proposed to consider such grossly nonstoichiometric oxides having different oxygen nonstoichiometry as chemical homologues participating in the oxygen exchange reaction and forming a series continuous in δ. The continuous homologous series approach is considered using the example of SrCo_0.9Ta_0.1O_3−δ, an SOFC cathode material. The equilibrium and kinetic properties of the oxide were studied by new methods of oxygen partial pressure relaxation and oxygen release. Linear free-energy relationships have been discovered in the homologous series: thermodynamic and kinetic enthalpy–entropy compensations, as well as the Brønsted–Evans–Polanyi relation. A relationship has been established between the change in the observed LFERs and the morphotropic phase transition in the oxide.