The kinetics of the isotope exchange between gaseous oxygen enriched with the 18O isotope and two LaMnO3+δ oxide samples - a nanopowder and a bulk nanocrystal - has been studied. The 18O isotope concentration has been measured by the acceleration nuclear microanalysis method. The coefficients of the volume and the nanograin boundary self-diffusion of oxygen have been evaluated at 500°C They are equal to 3.5·10 -20 and 1.5·10-13 cm2/s, respectively.