The interactions between water and the actinide oxides UO2 and PuO2 are important both fundamentally and when considering the long-term storage of spent nuclear fuel. However, experimental studies in this area are severely limited by the intense radioactivity of plutonium, and hence, we have recently begun to investigate these interactions computationally. In this paper, we report the results of plane-wave density functional theory calculations of the interaction of water with the {111}, {110}, and {100} surfaces of UO2 and PuO2, using a Hubbard-corrected potential (PBE + U) approach to account for the strongly correlated 5f electrons. We find a mix of molecular and dissociative water adsorption to be most stable on the {111} surface, whereas the fully dissociative water adsorption is most stable on the {110} and {100} surfaces, leading to a fully hydroxylated monolayer. From these results, we derive water desorption temperatures at various pressures for the different surfaces. These increase in the order {111} < {110} < {100}, and these data are used to propose an alternative interpretation for the two experimentally determined temperature ranges for water desorption from PuO2.