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The zero-field splittings for Mn2+ and Fe3+ impurity centres in ZnO crystals are investigated by using the high-order perturbation formula based on the strong-field scheme and the spin-orbit coupling mechanism. From these studies, it is found that the Mn2+ or Fe3+ ion should not occupy exactly the host Zn2+ sites, but is displaced along the C-3 axis by a distance DeltaR. The displacement and the related structural parameters in the Mn2+ or Fe3+ defect centre in ZnO are verified by the Newman's superposition model.