The local structure and the electron paramagnetic resonance (EPR) parameters (g factors and hyperfine structure constants) for the trigonal Nd 3+ centre in CdS are theoretically investigated by considering the local lattice relaxation. The impurity Nd 3+ is found not to occupy exactly the host Cd 2+ site, but to suffer a shift of about 0.31Å away from the sulphide triangle along the C 3 axis due to size and charge mismatch. The theoretical EPR parameters based on the above impurity axial displacement are in good agreement with the observed values. The local structure and the EPR parameters are discussed for this centre.