The title reactions were studied by measuring the oxygen isotope composition of H2O2 and O-2 produced by electron pulse irradiation and gamma-irradiation of solutions of N2O and BrO4- in water enriched with (H2O)-O-18. The fraction, xi, of the reaction O- + H2O --> OH- + OH that takes place by hydrogen atom transfer is found to be 0.22 +/- 0.02 at 22 degrees C and increases with temperature. The difference between the enthalpies of activation for hydrogen atom transfer and proton transfer is estimated to be 16 +/- 2 kJ mol(-1) and the corresponding entropy of activation at 22 degrees C to be 44 +/- 8 J K-1 mol(-1). A molecular model is sketched according to which 10-100 reversible proton transfers take place for each hydrogen atom transferred. Assuming no interference from impurities, the rate constant for the exchange reaction *OH + H2O --> H-2*O + OH is found to be 57 +/- 6 s(-1) at 30 degrees C.