The adsorption of NO on the (1 1 1) and (1 1 0) surfaces of ceria (CeO2) was studied using projector-augmented wave (PAW) method based density-functional theory within the generalized gradient approximation (GGA). Several adsorption sites for NO on the stoichiometric surfaces are found, all with weak molecule-surface interaction. The adsorption on the reduced surfaces is much stronger. The O-ends of the adsorbed NO molecules fill the oxygen vacancies and the N–O bonds are elongated. If two such adsorbed NO molecules, residing at neighbouring sites, meet, their N-ends will form a strong N–N bond with little or no barrier. This is an intermediate step towards dissociation of free N2 which is calculated to be strongly thermodynamically driven.