An attempt to explain the phenomenon of anomalous fast oxygen anion transport previously observed in the course of low temperatures topotactic oxidation of perovskite-related nonstoichiometric compounds has been made. According to the model developed the fast oxygen uptake relates to the high concentration of extended defects which exist in these compounds or can arise during oxidation. Experimentally observed specific kinetics has been described as being a result of fast oxygen transport taking place along the extended defects and followed by slow diffusion into undisturbed areas of the lattice.