Protonic spin-lattice relaxation times have been measured in crystalline CoCl2.6H2O in the temperature range 4.2-1.24°K, which includes the Néel transition region. Spin-echo experiments have also been carried out over this temperature range to determine the homogeneous transverse relaxation time T2 and the extent of the inhomogeneous broadening. All experiments in this series were performed with the position of the external field along the intermediate anisotropy axis (b). In the paramagnetic region, the spin-lattice relaxation time T1 and T2 became increasingly temperature-dependent below 3°K, changing most rapidly in the range 2.30-2.20°K. Moriya has pointed out that such rapid fluctuations in relaxation rates are to be associated with critical fluctuations in the electronic spin system. Below the Néel temperature TN, the protonic T1 is found to have a very strong temperature dependence. Below 2°K, T1~T-7. The observed temperature dependence of T1 in the antiferromagnetic state is in accord with theoretical predictions based on a magnetoelastic coupling between magnon and phonon modes. T2 exhibits much weaker temperature dependence below TN.