The EPR parameters of trivalent Er~(3+) ions doped in hexagonal Ga N crystal have been studied by diagonalizing the 364×364 complete energy matrices. The results indicate that the resonance ground states may be derived from the Kramers doublet Γ_6. The EPR g-factors may be ascribed to the stronger covalent bonding and nephelauxetic effects compared with other rare-earth doped complexes, as a result of the mismatch of ionic radii of the impurity Er~(3+)ion and the replaced Ga~(3+) ion apart from the intrinsic covalency of host Ga N. Furthermore, the J–J mixing effects on the EPR parameters from the high-lying manifolds have been evaluated. It is found that the dominant J–J mixing contribution is from the manifold ~2K_(15/2), which accounts for about 2.5%. The next important J–J contribution arises from the crystal–field mixture between the ground state ~4I_(15/2) and the first excited state~4I_(13/2), and is usually less than 0.2%. The contributions from the rest states may be ignored. The EPR parameters of trivalent Er ~ (3+) ions in hexagonal Ga N crystal have been studied by diagonalizing the 364 × 364 complete energy matrices. The results indicate that the resonance ground states may be derived from the Kramers doublet Γ_6. The EPR g-factors may be ascribed to the stronger covalent bonding and nephelauxetic effects compared with other rare-earth doped complexes, as a result of the mismatch of ionic radii of the impurity Er ~ (3 +) ion and replaced Ga ~ (3+ ) ion apart from the intrinsic covalency of host Ga N. Further, the J-J mixing effects on the EPR parameters from the high-lying manifolds have been evaluated. It is found that the dominant J-J mixing contribution is from the manifold ~ 2K_ (15/2), which accounts for about 2.5%. The next important J-J contribution arises from the crystal-field mixture between the ground state ~ 4I_ (15/2) and the first excited state ~ 4I_ (13/2 ), and is usually less than 0.2%. The contributions from the rest states may be ignored.