The photoluminescence spectra and luminescence excitation spectra (LESs) of n-type ZnSe single crystals annealed in LiCl melt is investigated in the temperature range from 82 to 420 K. It is established that such heat treatment of the crystals greatly decreases the intensity of the long-wavewlength luminescence bands and intensifies the edge radiation. The excitation spectrum of the long-wavelength photoluminescence bands contains several maxima near the fundamental and impurity absorption edges, it is shown that the complicated structure of the luminescence excitation spectra is due to relocation of a nonequilibrium hole from a shallow acceptor to a deeper acceptor by an Auger process with the participation of carriers localized at these centers.