The production of H-2 in the radiolysis of water adsorbed on micron-sized particles of CeO2 and ZrO2 has been examined. Radiation chemical yields of H-2 increase substantially with decreasing number of adsorbed water layers when the yield is determined with respect to the energy deposited directly by gamma-rays to the water. These yields reached values of 20 and 150 molecules of H-2 per 100 eV for one to two water layers on CeO2 and ZrO2, respectively, compared to 0.45 molecule/100 eV in bulk liquid water. The yields of H-2 determined with respect to the total energy deposited in both the oxide and water were found to have a smaller, but observable, dependence on the amount of water adsorbed. Radiolysis of ZrO2 With gamma-rays produced about 5 times more H-2 than CeO2 for the equivalent amount of water adsorbed. The results suggest that the increase in H-2 production is due to the transfer of energy, possibly by an exciton, from the oxide to the water. O-2 production was at least an order of magnitude less than H-2. The yield of H-2 in the 5 MeV helium ion radiolysis of water on CeO2 is the same as with gamma-rays, but the results with ZrO2 are substantially lower. The H-2 yields with helium ion radiolysis may be nearly independent of the type of oxide.