The emission spectra of Zn_1-x Mn_x Te/Zn _0.6Mg_0.4Te and Cd_1-x Mn_x Te/Cd _0.5Mg_0.5Te quantum-well structures with different manganese concentrations and quantum-well widths are studied at excitation power densities ranging from 10⁵ to 10⁷ Wcm^-2. Under strong optical pumping, intracenter luminescence of Mn²⁺ ions degrades as a result of the interaction of excited managanese ions with high-density excitons. This process is accompanied by a strong broadening of the emission band of quantum-well excitons due to the exciton-exciton interaction and saturation of the exciton ground state. Under pumping at a power density of 10⁵ W cm^-2, stimulated emission of quantum-well excitons arises in CdTe/Cd_0.5Mg_0.5Te. The luminescence kinetics of the quantum-well and barrier excitons is investigated with a high temporal resolution. The effect of the quantum-well width and the managanese concentration on the kinetics and band shape of the Mn²⁺ intracenter luminescence characterized by the contribution of the manganese interface ions is determined.