Spectroscopic methods are used to study the processes of accumulation of electron and hole trapping centers and energy transfer of electronic excitations to impurities in CaSO4-Mn and BaSO4-Mn. It is shown that the transfer of energy from the host to impurities occurs at the moment of charge transfer from the excited anionic complex SO_4^(2-) to the hybrid radiative electronic states at 2.95–3.1 eV formed from the electronic states of the Mn^(+)-SO_4^(-) and SO_4^(3-)-SO_4^(-) trapping centers. It was found that, in sulfates, under irradiation, as a result of charge transfer from excited anionic complexes of the host to the excited states of impurities Tl^(+),Cu^(+),Mn^(2+), hybrid radiative states emerge at 2.95–3.15 eV, occupying the same energy levels as the intrinsic electronic trapping center SO_4^(3-) of the host at 2.95–3.1 eV.