Nuclear magnetic resonance experiments have been performed in solid He3 at constant molar volumes in the α and β phases at various magnetic fields and temperatures by the spin-echo method. The self-diffusion coefficient D as well as the relaxation times T1 and T2 have been determined. D is observed to obey the Arrhenius equation as the temperature is lowered in the α phase, but at a low enough temperature it becomes temperature independent and depends only on the density. The activation energy for diffusion correlates well with that determined from specific heat measurements. At high magnetic fields T1 and T2 are observed to obey the Bloembergen, Purcell, and Pound relationships characteristic of relaxation caused by diffusion. At low magnetic fields, T1 becomes temperature independent as the temperature is lowered, and is observed to depend on magnetic field as exp(H2H02), implying that the relaxation is from Zeeman to exchange systems. Values of the exchange integral J are deduced from temperature-independent diffusion, field-dependent relaxation, and rigid-lattice values of T2, and show fair agreement internally. No agreement can be obtained with values of J deduced from observations of departures from Curie's law, the values here reported being much smaller. © 1963 The American Physical Society.