The interaction of gas-phase H atoms with ordered and disordered adlayers of atomic oxygen, hydroxyl, and molecular oxygen on Pt(111) surfaces was investigated by in situ mass spectrometry and post-reaction TPD (temperature programed desorption). Exposure of oxygen adlayers to gas-phase H atoms at 85 K leads to formation of H2O via two consecutive hydrogenation reactions: H(g)+O(a)-->OH(a) followed by H(g)+OH(a)-->H2O(g,a). Both reaction steps are highly exothermic, and nascent H2O molecules partially escape into the gas phase before being thermally accommodated on the surface. Empty surface sites and hydrogen bonding promote thermalization of H2O. Separate experiments performed with OH-covered Pt(111) surfaces reveal that the hydrogenation of hydroxyl is a slow reaction compared to the hydrogenation of atomic oxygen; additionally, the abstraction of H from OH by gas-phase D atoms, OH(a)+D(g)-->O(a)+HD(g), was detected. Abstraction of H from adsorbed H2O was not observed. Admission of gas-phase H atoms to O-2-covered Pt(111) surfaces at 85 K leads to the desorption of O-2 and H2O. The thermodynamic stability of the HO2 radical suggests that the reaction is initiated by hydrogenation of molecular oxygen, O-2(a)+H(g)-->HO2. The intermediate HO2 either decomposes via dissociation of the HO-O bond, HO2-->OH(a)+O(a), finally leading to the formation of H2O (similar to85%), or via dissociation of the H-O-2 bond thus leading to desorption of O-2 (similar to15%). The whole reaction sequence of formation and decomposition of HO2 is fast compared to the formation of H2O via hydrogenation of atomic oxygen and hydroxyl. The observed coverage dependence of the reaction kinetics indicates the dominance of hot-atom mediated reactions.