Control of cell number is critical in the development of all metazoans, in order to regulate the size of both the whole organism and its individual tissues and organs. This Thesis concentrates on cell number control in the developing central nervous system (CNS), using the oligodendrocyte lineage as a model. Oligodendrocytes are the myelinating cells of the CNS. In the spinal cord, their progenitors originate in the ventral neuroepithelium, before proliferating and migrating throughout the cord. Previous work has shown that platelet-derived growth factor (PDGF-)AA is crucial for oligodendrocyte progenitor proliferation. Furthermore, transgenic overexpression of PDGF-A in the murine CNS causes hyperproliferation of progenitors, demonstrating that the PDGF supply is limiting. The number of oligodendrocyte progenitors reaches a steady state before birth. In this Thesis I confirm the finding that the oligodendrocyte progenitor cell cycle slows down markedly as the population size reaches a plateau. Since this slowdown can be reversed by culturing the cells in saturating PDGF concentrations, it must reflect an extracellular and not an intracellular change in vivo. I show that PDGF concentration controls cell cycle time in vitro, suggesting that the crucial extracellular change might be a decrease in PDGF supply. By crossing two strains of PDGF-overexpressing transgenic mice I have generated offspring with a wide range of transgene copy numbers and corresponding levels of PDGF expression. Over this range, I have shown that PDGF supply controls progenitor number in a linear and unsaturable fashion. I have attempted to demonstrate a fall in PDGF concentration in the spinal cord directly by various methods, but have been unable to detect PDGF-A protein. These data are consistent with a model whereby progenitors deplete PDGF by receptor binding and internalisation. Thus, as cell numbers increase, PDGF availability falls and the population reaches a steady state when the rate of PDGF consumption by progenitors matches the rate of supply. This contrasts with models suggesting that an intracellular clock controls the timing of progenitor cell cycle withdrawal and differentiation.