O and Si donors in GaN are studied by Raman spectroscopy under hydrostatic pressure p. The ground state of O is found to transfer from a shallow level to a deep gap state at p{gt}20 GPa reminiscent of {ital DX} centers in GaAs. Transferred to Al{sub x}Ga {sub 1-x}N we predict that O induces a deep gap state for x{gt}0.40. In GaN:Si no such state is induced up to the highest pressure obtained (p=25 GPa ) equivalent to x=0.56 in Al{sub x}Ga {sub 1-x}N and possibly higher. We attribute this distinction to the lattice sites of the dopants. O substituting for N is found to be the origin of high free electron concentration in bulk GaN crystals. {copyright} {ital 1997} {ital The American Physical Society}