Comprehensive studies of the electrical properties of Mg-doped bulk GaN crystals, grown by high-pressure synthesis, were performed as a function of temperature up to 750 °C. Annealing of the samples in nitrogen ambient modifies qualitatively their resistivity values ρ and the ρ(T) variation. It was found that our material is characterized by a high concentration of oxygen-related donors and that the charge transport in the studied samples is determined by two types of states, one of shallow character (Mg-related state, EA≈0.15 eV), and the second one much more deep, E2≈0.95 eV (above the valence band). Depending on the effective concentration of either states, different resistivities ρ can be observed: lower resistivity (ρ≪104 Ω cm at ambient temperature) in samples with dominant EA states and very high resistivity (ρ≫106 Ω cm at ambient temperature) in samples with dominant E2 states. For the first type of samples, annealing at Tann≪500 °C leads to a decrease of their resistivity and is associated with an increase of the effective concentration of the shallow Mg acceptors. Annealing of both types of samples at temperatures between 600 and 750 °C leads to an increase of the deep state concentration. The presence of hydrogen ambient during annealing of the low-resistivity samples strongly influences their properties. The increase of the sample resistivity and an appearance of a local vibrational mode of hydrogen at 3125 cm-1 were observed. These effects can be removed- by annealing in hydrogen-free ambient. © 2001 American Institute of Physics.