High quality wurtzite GaN epilayers have been grown on ZnO(0001) substrates by reactive molecular beam epitaxy. Photoluminescence and reflectivity measurements point to high quality presumably due to the near match of both the crystal lattice parameter and the stacking order between GaN and ZnO. In addition, the good films lack the characteristic yellow photoluminescence band. Any misorientation of the GaN epilayer planes with respect to the ZnO substrate is not detectable with polarized reflectivity. The x-ray double crystal diffraction measurements indicate this misorientation is much smaller than those for GaN epilayers on SiC and Al2O3 . © 1997 American Institute of Physics.