The hippocampus-dependent "trace-appetitive conditioning task" increases cell proliferation and the generation of newborn young neurons. Evidence suggests that adult hippocampal neurogenesis and rapid eye movement (REM) sleep play an essential role in memory consolidation. On the other hand, REM sleep deprivation (REM-SD) induces detrimental effects on training-induced cell proliferation in the hippocampus's dentate gyrus (DG). Nonetheless, the role of REM sleep in the traceappetitive memory and fate determination of the newly proliferated cells is not known. Here, we have studied the following: (I) the effects of 24 h of REM-SD (soon after training) on trace-and delay-appetitive memory and cell proliferation in the adult DG and (II) the effects of chronic (96 h) REM-SD (3 days after the training, the period in which newly generated cells progressed toward the neuronal lineage) on trace-appetitive memory and the generation of newborn young neurons. We used a modified multiple platform method for the selective REM-SD without altering non-REM (NREM) sleep. We found that 24 h of REM-SD, soon after trace-conditioning, impaired the trace-appetitive memory and the training-induced cell proliferation. Nevertheless, 96 h of REM-SD (3 days after the training) did not impair trace memory. Interestingly, 96 h of REM-SD altered the generation of newborn young neurons. These results suggest that REM sleep plays an essential role in training-induced cell proliferation and the fate determination of the newly generated cells toward the neuronal lineage.