The wide bandgap II-VI semiconductors have unique properties which allow the possibility of suppressing the exciton-phonon scattering up to room temperature in quantum well structures designed so that the exciton excitation E1s?2s > h?LO. In particular, magnetic field and temperature dependent measurements are used to study the exciton binding energies and to investigate the exciton-LO phonon scattering processes of high quality ZnSe quantum wells in MgS grown by MBE. The small inhomogeneous broadening of the exciton transitions in these samples allows the observation of higher excited exciton states. Due to the large difference in band gap between ZnSe and MgS the exciton binding energy in a 5 nm well is found to be 43.9 meV, which is the largest reported for this material system. The FWHM of the heavy hole absorption transitions measured as a function of temperature shows that the scattering of the excitons by the LO phonons is partially suppressed. These results are compared with ZnS quantum wells where the exciton g-values have been measured and the exciton binding energies have been deduced from the exciton diamagnetic shifts. The results show the possibility of suppressing exciton-LO phonon scattering in these structures.