Based on transient nucleation theory, a numerical model has been constructed to describe the nucleation process of a new phase in front of the liquid-solid interface of a prior steady-growth phase in peritectic alloy with the combination of the concentration field calculated by a self-consistent numerical model for cellular/dendritic growth. The results show that the nucleation incubation time of a new phase varies with the solidification rate during unidirectional solidification. During unidirectional solidification of the Zn-4.0 wt.% Cu alloy, the incubation time changes very slightly when the solidification rate increases from 50 to 500 mu m/s, but it increases significantly when the solidification rate exceeds 500 mu m/s. The calculated results show a reasonable agreement with the experimental ones. This model reveals that nucleation of a new phase is time-dependent and reasonably explains the effect of the solidification velocity on the behaviors of nucleation and growth of epsilon dendrites in the matrix of the eta phase in unidirectional solidification of Zn rich Zn-Cu alloys.