The results of an investigation on oxidation processes in Mo/Be multilayer nanofilms are presented. The films annealed both in ambient atmosphere and in vacuum. The extreme ultraviolet (EUV) and X-ray reflectivity of the samples at 11.34 and at 0.154 nm respectively were measured before and after the treatment. No noticeable changes in film thicknesses and boundaries were observed during the annealing at temperatures up to 300°C. An oxidation mechanism of the nanofilms Mo/Be is established and the activation energy of the oxidation process is estimated to be 38 kJ/mol. To determine an absolute quantity of oxygen in the oxidized layers, a simple technique based on the EUV reflectivity data is proposed, and the range of its applicability is subsequently analysed.