[en] The starting point for this report is the discrepancy reported in previous work between the reaction-diffusion calculations and the CEX-1 experiment, which involves storage of defected fuel elements in air at 150 deg C. This discrepancy is considerably diminished here by a more critical choice of theoretical parameters, and by taking into account the fact that different CEX-1 fuel elements were oxidized at very different rates and that the fuel element used previously for comparison with theoretical calculations actually underwent two limited-oxygen-supply cycles. Much better agreement is obtained here between the theory and the third, unlimited-air, storage period of the CEX-1 experiment. The approximate integral method is used extensively for the solution of the one-dimensional diffusion moving-boundary problems that may describe various storage periods of the CEX-1 experiment. In some cases it is easy to extend this method to arbitrary precision by using higher moments of the diffusion equation. Using this method, the validity of quasi-steady-state approximation is verified. Diffusion-controlled oxidation is also studied. In this case, for the unlimited oxygen supply, the integral method leads to an exact analytical solution for linear geometry, and to a good analytical approximation of the solution for the spherically symmetric geometry. These solutions may have some application in the analysis of experiments on the oxidation of small UO₂ fragments or powders when the individual UO₂ grains may be considered to be approximately spherical. (author). 23 refs., 5 tabs., 11 figs