Somatic stem/progenitor cells are active in embryonic tissues but quiescent in many adult tissues. The detailed mechanisms that regulate active versus quiescent stem cell states are largely unknown. In active neural stem cells, Hes1 expression oscillates and drives cyclic expression of the proneural gene Ascl1, which activates cell proliferation. Here, we found that in quiescent neural stem cells in the adult mouse brain, Hes1 levels are oscillatory, although the peaks and troughs are higher than those in active neural stem cells, causing Ascl1 expression to be continuously suppressed. Inactivation of Hes1 and its related genes up-regulates Ascl1 expression and increases neurogenesis. This causes rapid depletion of neural stem cells and premature termination of neurogenesis. Conversely, sustained Hes1 expression represses Ascl1, inhibits neurogenesis, and maintains quiescent neural stem cells. In contrast, induction of Ascl1 oscillations activates neural stem cells and increases neurogenesis in the adult mouse brain. Thus, Ascl1 oscillations, which normally depend on Hes1 oscillations, regulate the active state, while high Hes1 expression and resultant Ascl1 suppression promote quiescence in neural stem cells.