The results of measurements of the bulk diffusion of tracer oxygen atoms in the oxides LnMnO3+δ (Ln = La, Nd, Sm) in the temperature range 400 – 750°С are presented. The measurements were carried out on micro-and nanopowders. Nanoscale powders were prepared by mechanical activation. A method based on the study of the kinetics of oxygen isotope exchange between the powder and gaseous oxygen enriched with 18O isotope was used to obtain data on the diffusion coefficients. The average concentration of 18O isotope in the powders was measured using NRA technique. The obtained diffusion coefficients lay in the range of 10-21 - 10-24 m2/s, the diffusion activation energy for all the oxides have been close to 1 eV. These results suggest that the migration of tracer oxygen in oxides LаMnO3+δ, NdMnO3+δ and SmMnO3+δ at low temperatures is realized via structural defects. As for the oxide LaMnO3+δ, its oxygen diffusion coefficients at low temperatures have been lower than the values extrapolated from high temperatures. Such behavior of diffusion properties has not been previously observed in other metal oxides. In this regard, the vacancy formation energy in the rare earth manganites has been supposed to increase with decreasing temperature.