We studied photoluminescence from melt-grown ZnO crystals annealed in air ambient at different temperatures. Along with intense and sharp excitonic lines, we observed several broad bands presumably related to deep acceptors. Two luminescence bands peaking at 1.95 and 2.15 eV at 10 K were studied in detail at different temperatures. The 1.95 eV band has been attributed to transitions from shallow donors to yet unidentified deep acceptor. Very slow non-exponential decay of this band at low temperatures supports such an assumption.