The spin-lattice relaxation time, T-1, and the spin-spin relaxation time, T-2, for H-1 and Rb-87 nuclei in Rb2Co(SO4)(2)center dot 6H(2)O crystals were investigated. The phase transitions occur near 370 K (=T-C1), 402 K (=T-C2), 413 K (=T-C3), and 458 K (=T-C4). The Rb-87 spectrum changes near T-C1 from Rb(1) and Rb(2) central resonance lines to one Rb central resonance line, and this change is due to the structural phase transition. The change in the H-1 T-C1 near T-C1 and the changes in T-1 and T-2 for Rb(1) and Rb(2) near T-C1 and T-C2 are also due to the phase transitions, and are related to changes in the symmetry of the octahedra of water molecules and slight rotations of the SO4 tetrahedra surrounding Rb+. Further, below T-C1 the spin-lattice relaxation rates, T-1(-1), for Rb(1) and Rb(2) are proportional to T-2, which implies that these relaxations occur mainly via Raman processes. (C) 2009 Elsevier Ltd. All rights reserved.