A new model for the case of a superposition of a phase transformation and a microstructure transition from columnar plane front to equiaxed dendritic growth for peritectic alloys is presented. This model is applied to Fe-Ni alloys where a phase transition from gamma to delta takes place when the solute content decreases. The results of the model are compared with predictions of the nucleation constitutional undercooling model. They show that the peritectic two-(solid) phase region is restricted and may completely disappear depending on nucleation undercooling and dendrite growth kinetics.