We studied the epitaxial growth of CeO2 thin films as a function of deposition temperature (300-850 degreesC) and film thickness (100-900 nm). The films were grown on YSZ(100), MgO(100) and Al2O3(1 (1) over bar 02) (r-plane sapphire) substrates by reactive d.c. magnetron sputtering of a cerium metal target in an Ar/O-2 plasma. The crystalline quality and biaxial alignment of the films were investigated using X-ray diffraction techniques (theta - 2 theta, omega -scans, pole figures, phi -scans) to determine the degree of c-axis (out-of-plane) and in-plane alignments given by the FWHM Deltaw and Delta phi, respectively. The CeO2/YSZ(100) heteroepitaxy occurred below 300 degreesC while deposition at higher temperatures resulted in single-crystal quality CeO2 films with Delta omega = 0.1 degrees and Delta phi = 0.2 degrees at 650-750 degreesC. The CeO2/MgO(100) and CeO2/Al2O3(1 (1) over bar 02) heteroepitaxy was evident at 600 degreesC and developed to nearly perfect biaxial alignment at 850 degreesC with Delta omega = 1 degrees and Delta phi = 5 degrees for CeO2/MgO(100), and Delta omega = 5 degrees and Delta phi = 9 degrees for CeO2/Al2O3(1 (1) over bar 02).