The interaction between gas-phase oxygen and LSM−YSZ (LSM is La 0.6 Sr 0.4 MnO 3±δ ; YSZ is ZrO 2 •Y 2 O 3 electrolyte) composite catalytic materials was studied by the in situ method based on isotope equilibration with the gas phase at T = 600−850 °C and pO 2 = 0.2−1.3 kPa. We made an attempt to develop mathematical criteria to prove the appearance of the spillover effect [migration of adsorbed particles from the active phase to triple-phase boundary (TPB)] from the experimental data. The heterogeneous exchange rate (r H ) and the three exchange types (r 0 , r 1 , r 2 ) were calculated, where 0, 1, and 2 differ in the number of surface oxide atoms participating during one elementary exchange act. The heterogeneous exchange rate for lanthanum−strontium manganite was 2.5−3 orders higher than the heterogeneous exchange rate for the zirconia-yttria electrolyte over the investigated temperature range. The exchange mechanism of composites LSM−YSZ was different from the LSM and YSZ oxides due to the fact that the ratios between the rates of the three exchange types of composites were also different from the individual phases. An original model was proposed for describing the kinetic dependences taking into account the oxygen exchange at LSM and YSZ individual oxides, at a TPB, and exchange between oxygen forms in an adsorption layer and at a TPB. It was shown, that at 600 °C, the exchange occurred without a significant effect of the exchange on TPB (r TPB ). The exchange on TPB became considerable with increasing temperature, so that at a temperature of 800 °C and higher, the rate-determining stage was the exchange between the forms of oxygen in the adsorption layer and on TPB, corresponding to the spillover effect. The phenomenon of the oxygen spillover effect on LSM−YSZ composites has been considered.