We have studied the quasi‐two‐dimensional exciton in ZnSe/ZnxMg1−xSySe1−y(x=0.85,y=0.21) single quantum wells (SQWs) by photoluminescence and photoluminescence excitation spectroscopy. Self‐consistent calculations of the peak energies for a series of SQWs give the conduction band discontinuity &Dgr;Ec=0.40&Dgr;Egand the binding energy of then=1 heavy‐hole excitonEb(hh1)=22.1 meV for an 8 nm well width. We believe that the binding energy of then=1 heavy‐hole exciton is smaller than the LO phonon energy our samples resulting in a very large exciton‐phonon interaction strength observed through the broadening of the exciton resonance with temperature. ©1995 American Institute of Physics.