A theoretical model has been proposed to describe the kinetics of oxygen isotopic exchange between gas and oxides with subsurface regions different from the bulk in the rate of oxygen transfer (surface phases, grain boundaries, etc.). Exact solutions valid for an arbitrary ratio between the exchange and diffusion rates have been obtained for both the time dependence of the total O-18 tracer concentration and the dependences of (OO)-O-16-O-16, (OO)-O-18-O-16, (OO)-O-18-O-18 molecules concentrations in a gas. The latter makes it possible to analyse the contributions to the kinetics from various types of exchange taking diffusion into account. The results obtained also allow the determination of the exchange rate and diffusivity from the experiment with high enough accuracy, as shown by the example of the oxide YBa2Cu3O6+x.