The interaction of atomic oxygen and nitrogen on the (0001) surface of corundum (α-alumina) is investigated from first-principles by means of periodic density functional calculations within the generalized gradient approximation. A large Al₂O₃ slab model (18 layers relaxing 10) ended with the most stable aluminium layer is used throughout the study. Geometries, adsorption energies and vibrational frequencies are calculated for several stationary points for two spin states at different sites over an 1 × 1 unit cell. Two stable adsorption minima over Al or in a bridge between Al and O surface atoms are found for oxygen and nitrogen, without activation energies. The oxygen adsorption (e.g., E_ad = 2.30 eV) seems to be much more important than for nitrogen (e.g., E_ad = 1.23 eV). Transition states for oxygen surface diffusion are characterized and present not very high-energy barriers. The computed geometries and adsorption energies are consistent with similar adsorption theoretical studies and related experimental data for O, N or α-alumina. The present results along with our previous results for β-cristobalite do not support the assumption of an equal E_ad for O and N over similar oxides, which is commonly used in some kinetic models to derive catalytic atomic recombination coefficients for atomic oxygen and nitrogen. The magnitude of O and N adsorption energies imply that Eley–Rideal and Langmuir–Hinshelwood reactions with these species will be exothermic, contrary to what happens for β-cristobalite.