The kinetics of the oxygen isotopic exchange between La0.7Sr0.3CoO3-delta and oxygen gas has been studied at on oxygen pressure of 1.28 x 10(3) Pa and temperatures from 786 to 875 degrees C. Experimental time dependencies of molecules (OO)-O-16-O-16, (OO)-O-18-O-16, (OO)-O-18-O-18 content in the gas phase have been analyzed by the method first proposed by the authors. Using this method we have directly calculated both the rates of the different types of surface exchange and the bulk diffusivity of oxygen from experimental data. It has been shown that under the experiment conditions at elevated temperatures the surface exchange proceed by the dissociative adsorption-desorption mechanism.