The carbon-13 spin-lattice relaxation times (T1) of glycine have been measured as a function of pD and concentration. Contrary to previously reported findings, no significant dependence was observed on either pD or concentration. In addition, the T1 values reported here are much longer than those published earlier. The discrepancies arise from the presence of paramagnetic impurities in the earlier samples. For the carboxyl carbon, dipole-dipole relaxation is dominant in both D2O and H2O solution, and in H2O there is a significant intermolecular dipolar contribution. Proton and oxygen relaxation times have also been measured. These, along with the carbon relaxation data, allow a discussion of the dynamics of glycine in solution.