In order to clarify impurity occupation and local structures for Cu 2+ in the CdS films, the g factors and hyperfine structure constants (HSCs) and their concentration dependences are theoretically studied from the perturbation calculations for both the cases of tetragonally compressed tetrahedral (TCT) and tetragonally elongated octahedral (TEO) 3d 9 clusters. Despite similar g anisotropies g // >g ⊥ >2, the calculated g factors and HSCs and their concentration dependences based on the TCT [CuS 4 ] 6− cluster show much better agreement with the experimental data than those based on the previously assigned TEO [CuS 6 ] 10− cluster. So, the g factors and HSCs can be ascribed to the substitutional TCT [CuS 4 ] 6− cluster on Cd 2+ site, and the possibility of the previous assignment of interstitial TEO [CuS 6 ] 10− cluster may be tentatively excluded. In the TCT [CuS 4 ] 6− clusters, the local Cu 2+ -S 2− bond angles θ related to C 4 axis are found to be about 1.54°larger than the ideal value θ 0 (≈54.736°) of a regular tetrahedron owing to the Jahn-Teller effect. The magnitudes of g factors and HSCs demonstrate the overall increasing trends with increasing Cu 2+ concentration, attributable to the decrease of covalency (increase of covalency factor N) and the increases of the angular deviation Δθ (=θ-θ 0 ) and the core polarization constant κ.