The spin Hamiltonian parameters of Gd 3+ in a single crystal of Thorium disulfide (TI1S2) are analysed by means of the superposition model, in its most general form of a two exponents power law. In fact, the approximated one exponent power law is not suitable for this compound, where the ion-ligand distances show a quite large spread. The results of the analysis are then applied to the case of Gd 3+ doped Thorium oxysulfide (ThOS), where the fitting of the experimental data is possible only assuming some distortion of the ligand cage.