In this letter, the authors report on the epitaxial growth by pulsed laser deposition of Sc2O3 and Er(5%):Sc2O3 films on {100} and {111} oriented Sc2O3. They observed layer-by-layer growth in the orientation defined by the substrate. This was indicated by reflection high energy electron diffraction as intensity oscillations of the specularly reflected electron beam. A monolayer-smooth film surface was observed by atomic force microscopy. Such a growth behavior was also achieved during initial growth of Sc2O3 on {100} oriented Y2O3. Additional x-ray diffraction analysis shows good agreement with the growth behavior mentioned above.