The adsorption of NO and NO2 molecules at the BaO surface has been investigated by means of density functional theory (DFT) cluster model calculations. Regular adsorption sites at flat terraces have been compared with those on steps and corners. The properties of the adsorbed molecules have been monitored by computing various observable properties, such as core level binding energies, hyperfine coupling constants, and vibrational frequencies. NO binds strongly at the oxide anions at terraces, steps, and corners of the BaO surface. The bonding has a substantial polarity due to delocalization of charge from the surface to the adsorbate, but cannot be described as a full charge transfer interaction. The spin is almost entirely localized on the NO adsorbed molecule. NO2 binds to the BaO surface in two different ways, N-down and O-down. In both orientations the oxide anion on the surface is oxidized with formation of an NO2- species which interacts electrostatically with the neighboring Ba cations. The spin is localized on the surface anions by the effect of the creation of a hole in the O(2p) valence shell. The O-down mode is more stable on terrace sites, while on low-coordinated sites the two orientations have similar stabilities. For both NO and NO2 the low-coordinated sites exhibit a much larger reactivity than the flat terraces. The formation of O- ions in the case of NO2 adsorption can be very important for the further reactivity of the surface.