An instability at solid-liquid interfaces induced by coherency strain has been studied in the Mo-Ni system. When the lattice parameter of a solid solution varies with compositions, a coherency strain develops if there is diffusion in the solid adjacent to the liquid. As a result of this strain, the originally planar solid-liquid interface becomes unstable by dissolution of the initial solid and precipitation of the new solid, forming a sinusoidal interface shape. In a previous study, the coherency strains have been shown to be the driving force for the instability. In this paper we analyze the evolution of the instability with time, from initiation to healing of the instability. Using the equations developed for liquid film migration (LFM) the change of microstructure is explained qualitatively. In addition, the relationships between this instability, diffusion induced grain boundary migration (DIGM) and LFM are discussed.