Using separate samples containing deuterated glucose and D2O, the motions of the glucose and the water molecules in the viscous liquid and in the amorphous glass phase of glucose/water mixtures are examined. Spin-lattice relaxation measurements and spectra obtained in the solid confirm the existence of both a crystalline ice phase and an amorphous glass phase. Diffusion measurements performed using the large gradient in the fringe field of a superconducting magnet determine the rates of translational motion of both the sugar and the water molecules over a limited range of temperature in the viscous liquid region. From the deuterium nuclear magnetic resonance spin-lattice relaxation time,T-1, the spin-spin relaxation time,T-2, and spin-alignment measurements, correlation times for the motion of these molecules are obtained. The correlation time for the alpha process increases dramatically at T-g, while the beta process continues into the low temperature glass phase, following an approximately Arrhenius relationship.