The structural phase transitions and relaxation processes of Cs2Co(SO4)(2)center dot 6H(2)O and Cs2Zn(SO4)(2)center dot 6H(2)O single crystals were investigated, with the phase transitions of both crystals being determined from NMR data. The spin-lattice relaxation time, T-1, of the Cs-133 nucleus in two crystals undergoes a significant change near the phase transition temperature, T-C, and these changes coincide with the changes in the splitting of the Cs-133 resonance lines. The variations in the temperature dependence for the splitting of the Cs-133 resonance lines and T-1 near T-C are related to changes in the symmetry of surrounding Cs+. In addition, the Cs-133 T-1 of Cs2Co(SO4)(2)center dot 6H(2)O, which contains paramagnetic ions, was found to be shorter than that of Cs2Zn(SO4)(2)center dot 6H(2)O. This relaxation time is inversely proportional to the square of the magnetic moment of the paramagnetic ions. The differences between the Cs-133 T-1 of these compounds are probably due to the differences between the electronic structures of their metal ions. (C) 2009 Elsevier B.V. All rights reserved.