Epitaxial films from one material, with sharp borders between contacting regions having different film orientation are grown on one surface of the substrate for the first time. The main reason for the deposition of thin ceria layers with mixed (001) and (111) orientations on a (<1(1)over bar 02>) sapphire substrate is determined. We suggest that this is related to the availability of surface defects which, in thin near-surface layers, deviate from stoichiometric composition. This in turn is connected with the loss of oxygen. A technique for influencing CeO2 film orientation is demonstrated. This involves specific preliminary processing of the substrate, and the selection of oxygen partial pressure during the deposition process. High quality thin (30-50 nm) "protective" (001) CeO2 epitaxial layers are prepared on (<1(1)over bar 02>) Al2O3. Structures comprising two epitaxial protective CeO2 layers, orientations (001) and (111), are made on the base of (0001) and (<1(1)over bar 02>) sapphire substrates. The interface between the epitaxial layers is <1 000 nm. Preliminary results using this method are described, and the possibility of creating a "bi-epitaxial" transition in thin YBa2Cu3O7-x layers is explored.