The nuclear spin relaxation rates in a number of alkali halides have been measured at temperatures above the melting point and in LiBr and LiI were found to be approximately proportional to the reciprocal of the temperature. The rates are explained by the interaction of the nuclear electric quadrupole moment with the field gradient of the surrounding ionic charge but, just as in the case of the quadrupole relaxation in solid alkali halides, the point-ion model for the calculation of the field gradients proved to be untenable. Approximate values for the mean-square gradients obtained from previous data taken in the solid state were used in conjunction with the present measurements to calculate a correlation time. This correlation time, which is the average time that the spatial configuration of a group of near neighbours persists in the liquid state, was found to be about 10-13 s.