In this, Part I of a two-part study, a generalized model for the oxidation of the ternary compounds, Tin+1AlXn, where n = 1-3 and X is carbon and/or nitrogen, is proposed. In all cases, the oxidation products in the 800-1100 degreesC temperature range are rutile TiO2, in which some Al is dissolved, i.e., (Ti1-yAly)O2-y/2, where y < 0.05 and Al2O3. The oxidation occurs by the inward diffusion of oxygen and the outward diffusion of Al3+ and Ti4+ ions through the (Ti1-yAly)O2-y/2 layer. The C and N atoms are presumed to diffuse through the reaction layers and oxidize. The basic premises of the model are that the subjection of the (Ti1-yAly)O2-y/2 layer to an oxygen chemical potential gradient results in its demixing, with the Al3+ dissolving into the rutile at the low oxygen partial pressure and its precipitation as Al2O3 at the high partial pressure side. If extensive, the demixing results in the formation of layers of porosity, through which the Al3+ ions cannot diffuse but the O2- ions can. The resulting microstructures can be highly striated where three layers; an Al2O3-rich layer, an (Ti1-yAly)O2-y/2-rich layer, and a porous layer repeat numerous times. Comparison with previously published results on the oxidation of Ti3SiC2 leaves little doubt that dissolution of the Al in the reaction layer enhances the oxidation kinetics. This is most probably accomplished by an increase in the oxygen vacancy concentration. The fact that the oxide scales are not fully dense is also believed to play an important role in enhancing the oxidation kinetics.