Optically-detected electron-nuclear double resonance (ODENDOR) studies at 24 GHz on high-resistivity GaN films grown on Al2O3 have been combined with x-ray diffraction measurements to obtain information on the location of the residual shallow donors. Strong ODENDOR assigned to 69,71Ga lattice nuclei was detected on the g=1.951 effective-mass donor resonance found on the 2.2 eV emission bands. The x-ray studies reveal that the layers are under biaxial compression with high values of strain (∼ 2–3 × 10−3). The quadrupole splittings for 69Ga are smaller than those reported for strain-free samples by 15–25 %. The dominant sources of the local electric field gradient (EFG) responsible for the splittings are attributed to the wurtzite crystal structure and the strain fields that arise from the lattice constant mismatch and the difference in thermal expansion coefficients. An EFG/strain relationship of 3 × 1022 Vm−2 per unit strain at the 69,71Ga nuclei is deduced. The ODENDOR can be described with asymmetry parameter η=0. This provides evidence that the donors are in the crystallites rather than near grain boundaries.