The adsorption of NHx fragments and oxidation of them by O and OH on the Rh(111) crystal surface have been studied using first-principles density-functional calculations. The stability and configurations of OHx and NHx have been investigated and characterized using frequency analysis. Several paths of NHx (x = 1-3) oxidation with O and OH and reverse elementary processes have been determined. The transition states have been determined and analyzed in detail. The activation barriers and thermodynamic and kinetic data have been calculated for all of the elementary steps. The calculations have shown that atomic oxygen does not promote ammonia decomposition. The elementary reactions with O are endothermic, and they have significant barriers, comparable with ammonia dehydrogenation barriers [Popa, C.; Offermans, W. K.; van Santen, R. A.; Jansen, A. P. J. Phys. Rev. B 2006, 74 (15), 155428-1-155428-10].1 The OH fragment does promote ammonia decomposition. The elementary reactions are exothermic or slightly endothermic, and the activation barriers are significantly lower. The activation entropies decrease the pre-exponential factors significantly. Nitrogen recombination on the Rh(111) surface has a high activation barrier, but it is comparable with the barriers on stepped surfaces of other metals. The first step of ammonia oxidation occurs late. The subsequent elementary steps are earlier and earlier from the geometrical point of view.