The temperature dependences of the self‐diffusion coefficient and the spin‐lattice relaxation time have been studied by NMR measurements performed on a good glass former LiCl‐6H2O. The spin‐lattice relaxation time can be separated into two relaxation processes, i.e., inter‐ and intramolecular processes. We have related these relaxation processes to the translational diffusion which corresponds to the primary or α‐relaxation and to the local motions which are related to the β‐relaxation in glass forming systems. The results throw some light to the evolution with temperature of these relaxation processes in the LiCl‐6H2O system over the normal liquid, supercooled liquid and glass sates.