The nuclear spin‐lattice relaxation timeT1of11Band23Na have been measured in the following insulating glasses: B2O3, Na2B4O7, (Na2O)0.3(SiO2)0.7. In all cases relaxation has been shown previously to be dominated by a strong quadrupolar mechanism.T1is observed to decrease between 1.2K and 273K and to be nearly field independent up to 55kG. In view of the available experimental results, the various models which have been proposed to account for NMR relaxation in glasses are shown to be unsatisfactory.