The spin-lattice relaxation time, T1, and the spin-spin relaxation time, T2, of He3 nuclei in liquid mixtures of He3 and He4 at 5%, 14% and 35% He3 concentrations have been measured. T1 and T2 values were also obtained for pure He3. The technique of adiabatic fast passage was employed to measure relative magnitudes of the magnetization. The results show that T1 and T2 tend to decrease as the temperature decreases below the lambda point of the mixtures. They show also that T1 and T2 decrease as the concentration of He3 decreases. The latter implies that impurity effects become more important the lower the He3 concentration is. A model based on bulk and wall impurities was used to explain the results. This model was also used to compute the diffusion coefficient for He3 in the three mixtures. The calculations show that the diffusion coefficient increases with decreasing He3 concentration and with decreasing temperature. This implies that the superfluid component of the He4 behaves as if it were a vacuum. Khalatnikov and Zharkov1 have calculated the diffusion coefficient of He3 in Hell on the basis of the Landau theory of superfluidity. The experimentally determined diffusion coefficients are in good agreement with this theory.