The paper presents the results of structural studies of CeO2 buffer layers grown by pulsed laser deposition on single-crystal substrates of r-Al2O3 ( ) at a substrate temperature of 750C. It was shown experimentally that when the oxygen pressure changes during growth, while maintaining the remaining growth parameters unchanged, it is possible to obtain buffer layers with different crystallographic orientations: at an oxygen pressure of 0.002 mbar, the buffer layers have an orientation of (111), and at an oxygen pressure of 0.2 mbar (002). The results obtained may be of interest for the preparation of epitaxial films and nanoheterostructures with layers of high-temperature superconductors and doped manganites on r-Al2O3 single-crystal substrates with CeO2 buffer layers.