When a 90Mo-10Ni alloy (by wt) liquid phase sintered at 1400-degrees-C is heat-treated at 1400-degrees-C after replacing the matrix with a melt of 44Ni-34Mo-22W (by wt), the liquid films between the grains migrate, leaving behind an Mo alloy enriched with W. The ratio of the lattice diffusivity of W in Mo, D, to the initial migration velocity, upsilon, (D/upsilon) is estimated to be between 0.03 and 0.18 angstrom. Hence, it appears that there is no lattice diffusion of W ahead of the migrating liquid film, and in such a case the driving force has been suggested to be the chemical free energy. But the observed v is approximately same as that to be expected if the driving force is assumed to be diffusional coherency strain energy. Likewise, a previous study of den Broeder and Nakahara shows that the rate of chemically-induced grain boundary migration in Cu-Ni shows a smooth variation with temperature as D/upsilon decreases from values much larger than the interatomic spacing to values much smaller with decreasing temperature. The coherency strain energy thus appears to be a general driving force for the migration even when the apparent diffusion length indicated by D/upsilon is smaller than the interatomic spacing.