The physics and chemistry of the actinide elements form the scientific basis for rational handling of nuclear materials. In recent experiments, most unexpectedly, plutonium dioxide has been found to react with water to form higher oxides up to PuO(2.27), whereas PuO(2) had always been thought to be the highest stable oxide of plutonium. We perform a theoretical analysis of this complicated situation on the basis of total energies calculated within density functional theory combined with well-established thermodynamic data. The reactions of PuO(2) with either O(2) or H(2)O to form PuO(2+delta) are calculated to be endothermic: that is, in order to occur they require a supply of energy. However, our calculations show that PuO(2+delta) can be formed, as an intermediate product, by reactions with the products of radiolysis of water, such as H(2)O(2).