The electrical properties of epitaxial ZnO thin films grown on sapphire substrates by pulsed laser deposition were investigated by temperature dependent Hall measurents. The thin films investigated were grown at different oxygen partial pressures ranging from 10-2 mbar to 1 mbar. The formation of a degenerate layer, determining the low temperature Hall data, depends on the oxygen partial pressure applied during growth. Further, the formation of such a layer can be correlated to the grain size of the samples. The thermal activation energy of dominant donors decreases in tendency with increasing oxygen partial pressure p(O2); it is about 100 meV for p(O2) ≤ 3 × 10-2 mbar and about 30 meV for p(O2) ≥ 0.1 mar. The concentration of donors and compensating acceptors increases with increasing p(O2).