The physics and chemistry of the actinide elements form the scientific basis for rational handling of nuclear materials(1-3). In recent experiments(4), most unexpectedly, plutonium dioxide has been found to react with water to form higher oxides up to PuO2.27, whereas PuO2 had always been thought to be the highest stable oxide of plutonium(2,3). We perform a theoretical analysis of this complicated situation on the basis of total energies calculated within density functional theory(5,6) combined with well-established thermodynamic data. The reactions of PuO2 with either O-2 or H2O to form PuO2+delta are calculated to be endothermic: that is, in order to occur they require a supply of energy. However, our calculations show that PuO2+delta can be formed, as an intermediate product, by reactions with the products of radiolysis of water, such as H2O2.