We present phase-field simulations of isothermal phase transformations in the peritectic system below and above the peritectic temperature TP , and in the monotectic system below the monotectic temperature TM. We focus particularly on the Liquid-Film-Migration (LFM) mechanism, which appears to be the generic process for phase transformations above TP . Below TP , we obtain an assymetric LFM, suggesting the existence of a doublon structure in free space. In the monotectic system, the transformation from a liquid L1 to a solid+liquid L2 mixture proceeds via the migration of a L2 film, which is the analogous of the LFM process. When the metastable state consists of a liquid-liquid mixture, a dendritic-like solidification is obtained.