The asymmetric line shape of the transient photoluminescence (PL) spectra of high-quality Zn1−x−yMgxCdySe epilayers is deconvoluted to a narrow and a broad Gaussian peak at each time delay. The fitted energy difference between the two peaks corresponds to one longitudinal optical (LO) phonon energy. We assign the narrow peak to the recombination of free excitons (FXs) and the broad peak to the recombination of excitons localized in the broad band tail characteristic for this quaternary compound. The broad PL peak is found to arise from the energy relaxation of the FX at the exciton mobility edge to the localized states by LO phonon emission. Therefore, the population peak of the localized excitons is formed at one LO phonon energy below the FX for all times after the laser excitation.