Many types of vertebrate precursor cells divide a limited number of times before they stop and terminally differentiate. In no case is it known what causes them to stop dividing. We have been studying this problem in the proliferating precursor cells that give rise to post‐mitotic oligodendrocytes, the cells that make myelin in the central nervous system. We show here that two components of the cell cycle control system, cyclin D1 and the Cdc2 kinase, are present in the proliferating precursor cells but not in differentiated oligodendrocytes, suggesting that the control system is dismantled in the oligodendrocytes. More importantly, we show that the cyclin‐dependent kinase (Cdk) inhibitor p27 progressively accumulates in the precursor cells as they proliferate and is present at high levels in oligodendrocytes. Our findings are consistent with the possibility that the accumulation of p27 is part of both the intrinsic counting mechanism that determines when precursor cell proliferation stops and differentiation begins and the effector mechanism that arrests the cell cycle when the counting mechanism indicates it is time. The recent findings of others that p27‐deficient mice have an increased number of cells in all of the organs examined suggest that this function of p27 is not restricted to the oligodendrocyte cell lineage.