The EPR parameters (D, g‖andg⊥) for V2+, Ni2+and Mn2+ions in linear-chain lattice CsMgCl3at 77 K have been studied from the crystal-field theory. From these studies, one can find that the local lattice relaxation occurs in the vicinity of these paramagnetic impurity ions. The bonding angles β of MCl4-6groups in the cases of V2+and Ni2+ions are determined quantitatively from EPR data and in the case of Mn2+ion, it is estimated qualitatively. These results support the opinion that the [MX−3]nchains in one-dimensional AMX3, lattice are easily deformed to accommodate impurity ions.