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The impurity displacements and the g factors g(parallel to) and g(perpendicular to) of the two tetragonal Ni3+ centres (I and II) in SrTiO3 are theoretically investigated by using the perturbation formulae of the g factors for a 3d(7) ion with low spin (S = 1/2) in tetragonally distorted octahedra. In these formulae, the contributions to the g factors from the tetragonal distortion, the ligand spin - orbit coupling coefficient, and the ligand orbitals, which were usually neglected in previous studies (Muller K A et al 1969 Phys. Rev. B 186 361; Lacroix R et al 1964 Helv. Phys. Acta 37 627), are taken into account based on the cluster approach. Centre I ( or II) was ascribed to the substitutional Ni3+ at the Ti4+ site, associated with the nearest neighbour oxygen vacancy V-O (or the near neutral V-O -(- 2e)) along the C-4 axis as a compensator. The impurity Ni3+ is found to shift away from ( or towards) the compensator by about 0.033 nm ( or 0.010 nm) along the C-4 axis, respectively. As a result, the ligand octahedron around the impurity is elongated ( compressed) in centre I ( II), corresponding to the negative ( positive) anisotropy Delta g (= g(parallel to) - g(perpendicular to)). The theoretical g factors based on the above impurity displacements show good agreement with the observed values.