The non-equilibrium solidification behaviors of undercooled Ni81P19 eutectic melts have been analyzed with respect to microstructure formation and transition during fluxing process of undercooled melts. A series of microstructure transitions far from equilibrium are found with increasing undercooling of the melt. Transitions from regular (rod) to anomalous eutectic to cellular eutectic regions are revealed beyond a critical undercooling. In order to explain formation and growth of anomalous eutectic, a model has been proposed which describes remelting of the primarily formed eutectics phase with dendrite characteristic due to instability of the dendrite morphology. The solid/liquid interfacial energy has been discussed to demonstrate formation of thin cellular eutectic regions if the udercooling passes certain higher critical undercooling. (C) 2003 Published by Elsevier Science B.V.