A double cascade-type four-level multiple-quantum-well-based exciton–biexciton transitions are proposed. The study is carried out on a 4.8-nm ZnSe single-quantum well which is embedded into ZnMgSSe cladding layers and pseudomorphically grown by molecular beam epitaxy on a(0 0 1) GaAs substrate. It is displayed that the exciton spin relaxation and relative phases between applied fields can influence the transient and steady-state behaviors of absorption, dispersion, and group velocity of two weak probe and signal fields. Also, transient behaviors of electron population of different levels are discussed. It is found that the probe or signal amplification occurs in the absence of population inversion. A double cascade-type four-level multiple-quantum-well-based exciton-biexciton transitions are proposed. The study is carried out on a 4.8-nm ZnSe single-quantum well which is embedded into ZnMgSSe cladding layers and pseudomorphically grown by molecular beam epitaxy on a (0 0 1) GaAs substrate. It is displayed that the exciton spin relaxation and relative phases between applied fields can influence the transient and steady-state behaviors of absorption, dispersion, and group velocity of two weak probes and signal fields. Also, transient behaviors of electron population of different levels are discussed. It is found that the probe or signal amplification occurs in the absence of population inversion.