Measurements of T1 and T2, the spin-lattice and spin-spin relaxation times, are reported for Li7 and F19 nuclei in a single crystal of LiF. T1(Li) has been measured from room temperature to the melting point (1120K) and the other quantities from 830K to the melting point. Above 620K, relaxation is caused exclusively by the diffusion of Li and F ions. T1(Li), T2(Li), and T1(F) are mainly determined by νLi, the jump frequency of Li ions, and T2(F) mainly by νF. Using a theory of relaxation developed elsewhere, νLi and νF are obtained for the region of intrinsic diffusion as νLi=1.7×1016exp(-1.81eV/kT) and νF=4.5×1017exp(-2.2eV/kT). For the extrinsic region, the motional activation energy of Li ions is obtained as 0.71 eV. The values of νLi are in good agreement with those obtained from conductivity measurements; to our knowledge, νF has never been measured by other methods. Below 620K quadrupolar relaxation due to lattice vibrations and relaxation by paramagnetic impurities become important, and rough values are obtained for these contributions to T1(Li). Large angular variations of T1 and T2 are observed in the region of relaxation due to atomic diffusion. T2(Li) and T1(Li) vary by a factor of 2 and 1.5, respectively, as a function of crystal orientation, in good agreement with theoretical prediction. A crude measurement of T1(Li) in molten LiF is discussed. © 1963 The American Physical Society.