The formation of a terrace-step surface nanostructure disoriented with respect to the R-plane on sapphire crystals is studied. The possibility of the formation of atomically smooth steps with a height about 0.34 nm is shown. This size corresponds to the interplanar distance of 0.34 nm along the direction [012] in a sapphire crystal. The substrates prepared in such a way are used in the course of the epitaxy of Fe2O3 and In2O3 films. A method of a high-temperature oxidation of previously deposited iron and indium films under atmospheric conditions is used. It is shown that the structural and geometrical similarity of Fe2O3 and sapphire crystal lattices promotes the growth of epitaxial films aligned with respect to the substrate. It is determined that the stress occurring in the growing In2O3 films in the course of oxidation and solid-phase epitaxy, as well as owing to a discrepancy between the lattice parameters at the film–substrate interface, is insufficient for the formation of the metastable rhombohedral In2O3 phase. The influence of terrace-step nanostructure of the surface of substrates at the initial stages of the growth of epitaxial films is discussed.