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The perturbation formulas of the EPR g factors g,, g and g. for a 4f(11) 1 ion in orthorhombic symmetry are established. In these formulas, the contributions to the g factors arising from the second-order perturbation terms and the admixture of various states are taken into account. The above formulas are applied to the orthorhombic Er3+ centers in YAG, YGG and LuGG garnets. By analyzing their g factors, we find that the polar angles theta(j)(') of the impurity-ligand bonds related to the Z axis of the crystals in these Er3+ centers are smaller than the host angles theta(j) in pure crystals, whereas the azimuthal angles, related to the X axis in the impurity centers are larger than the corresponding phi(j) in the hosts. The g factors and their anisotropies Delta g [= g(z) - (g(x) + g(y))/2] and delta g (= g(x) - g(y)) for Er3+ in the garnets based on the above local structural parameters are in good agreement with the observed values. In addition, the angular distortions Delta theta (= theta(j)(') - theta(j)) or Delta phi (= phi(j)(') - phi(j)) obtained by analyzing the EPR data in this work are different from Delta theta(2), or Delta phi(2) (for only the second set of ligands, i.e., j = 2) based on the superposition model crystal-field analysis in the previous work. The validity of the results is discussed. (c) 2004 Elsevier B.V. All rights reserved.