In many vertebrate cell lineages, precursor cells divide a limited number of times before they arrest and terminally differentiate into postmitotic cells. It is not known what causes them to stop dividing. We have been studying the 'stopping' mechanism in the proliferating precursor cells that give rise to oligodendrocytes, the cells that make myelin in the central nervous system. We showed previously that the cyclin-dependent kinase inhibitor p27Kip1 (p27) progressively accumulates in cultured precursor cells as they proliferate and that the time course of the increase is consistent with the possibility that p27 accumulation is part of a cell-intrinsic timer that arrests the cell cycle and initiates differentiation at the appropriate time.