A theoretical description of the three-pulse photon echo peak shift for model reaction systems is presented. An electronic two-state system with a finite upper-state lifetime and a three-state system in which electronic transitions can occur are considered. A probabilistic argument is employed to incorporate the incoherent transitions. New pathways describing the transition of electronic population are introduced and the nuclear propagator in the electronic population state is written by a convolution integral between those of the nonreactive two-state system weighted by some factors for the electronic transition. The response functions are given by multitime correlation functions and are analyzed by the cumulant expansion method. Some numerical calculations are presented and the influence of incoherent reactions on the peak shift is discussed. Comparison with experimental data confirms the existence of the effects predicted here.