The free radicals produced by gamma irradiation in the polymer network are formed with ionizing radiation. The decay rates of radicals in the temperature range were used to estimate the diffusion coefficient of oxygen into polymeric spheres by an electron spin resonance (ESR) technique. The ESR results showed that the activation energy of the diffusion of oxygen into poly(methyl methacrylate) (PMMA) in the temperature range 10-40 degrees C is 29.6 kJ/mol. There are two activation energies of the diffusion of oxygen into poly(vinyl acetate) (PVAc) in the temperature range 25-50 degrees C. The activation energies below and above 35 degrees C, which is the glass transition temperature of PVAc, were found to be 16.8 and 82.5 kJ/mol, respectively.