The QPI (quasiparticle injection) devices have the most transistor-like characteristics in many superconducting three-terminal devices. In particular, Quiteron which operates with the principle of energy gap's suppression only to modulate the conductance of the output junction has a promising feature, such as a large gain, non-latching operation, and binary inversion. In this paper, we have investigated the behavior of the energy gaps to analyze the characteristics of the QPI devices. First we have introduced the nonequilibrium GL equation. Then we have derived a set of equations for QPI devices by using this equation. It is found that the energy gap of middle layer has the singularity under quasiparticle injection.