Alkaline earth oxides are leading candidates as NOx (x = 1, 2) sorbents; however, the understanding of adsorption and reaction of NOx on these surfaces is currently limited. In this paper, Mg(001) terrace cluster models and density functional theory (DFT) are used to characterize the adsorption properties of neutral and charged NO, NO2, and NO3. Neutral NO and NO2 molecules weakly adsorb on the MgO terrace, while neutral NO3 adsorbs more strongly through oxidation and significant acid-base coordination with the surface. Chemisorbed nitrite can be formed either from adsorption of Lewis acidic NO+ on Lewis base surface sites (O-s(2-)) or from adsorption of Lewis basic NO2-on Lewis acid surface sites (Mg-s(2+)). Similarly, chemisorbed nitrate can form from NO2+ adsorption on O-s(2-) Sites or NO3-adsorption on Mg-s(2+) sites. These charged adsorbates are not expected to exist in isolation on the MgO surface but rather are expected to form oppositely charged, cooperatively bound pairs with enhanced adsorption energy over the isolated neutrals. While results are demonstrated for adsorption on MgO, they have application to NOx adsorption on a wide range of oxide surfaces.