Epitaxial, single-crystal films of ZrO2 (Y2O3) were formed on (100) oriented single crystal substrates of ZrO2 (9.5 mol% Y2O3) using water-based solutions of zirconium acetate and yttrium nitrate as a precursor. Film compostions of ZrO2 (0 - 40 mol% Y2O3) were examined; since the lattice parameter of ZrO2 (Y2O3) increases with yttria content, the lattice mismatch was systematically varied to a maximum of 1.5%. Precursor films were deposited by spin coating, pyrolyzed, and held for 1 hour at 900°C, 1000°C, and 1100°C. X-ray diffraction showed that a strongly oriented film had developed after pyrolysis of the precursor. In addition, all samples, except those treated at 1100°C containing 6 – 15 mol% Y2O3, gave (111) peaks, indicating film polycrystallinity. Electron back-scattering patterns showed that epitaxial single crystals were formed at 1100°C for films containing 3 – 20 mol% Y2O3. Scanning electron microscopy showed that the epitaxial films had a porous structure. These results indicate that the epitaxy is a two-stage process: oriented nucleation upon pyrolysis, followed, for low mismatches, by subsequent consolidation into a single-crystal film above 1000°C.