Comparisons are made between theoretical and experimental rates of boundary migration during grain growth in zone-refined metals; these indicate that a single-atom process is involved. A model is proposed for the mechanism of grain-boundary migration based on the assumption of a single-atom process and the fact that the energies of activation for grain growth, both in zone-refined lead and tin, are similar to the energy barrier to be overcome by an atom in transferring from the solid to the liquid state during melting.