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The local structures of the two trigonal Er3+ (Er-167) centers I and II in KMgF3 are theoretically studied using the perturbation formulas of the g factors for a 4f(II) ion in trigonal symmetry. In these formulas the contributions to the g factors from the second-order perturbation terms and admixtures of various states are taken into account. Based on the studies, the centers I and II are attributed to, respectively, the Er3+ impurity occupying the octahedral Mg2+ site with a K+ vacancy V-K and the dodecahedral K+ site with a Mg2+ vacancy V-Mg along the C-3 axis due to charge compensation. According to the calculations. the Er3+ ion in either center is found to undergo an axial displacement DeltaZ(L) (L = I or II) towards the compensator (V-K or V-Mg) along the C-3 axis-because of electrostatic attraction. The calculated g factors for both the Er3+ centers based on the displacements DeltaZ(L) show reasonable agreement with the observed values. The local structures of the two centers are discussed. The theoretical studies in this paper may be useful for understanding the optical properties of Er3+-doped KMgF3. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.