After many years of research, the mechanisms that generate a periodic pattern of repeated elements (somites) along the length of the embryonic body axis is still one of the major unresolved problems in developmental biology. Here we present a mathematical formulation of the cell cycle model for somitogenesis proposed in Development 105 (1989), 119-130. Somite precursor cells in the node are asynchronous, and therefore, as a population, generate continuously pre-somite cells which enter the segmental plate. The model makes the hypothesis that there exists a time window within the cell cycle, making up one-seventh of the cycle, which gates the pre-somite cells so that they make somites discretely, seven per cycle. We show that the model can indeed account for the.spatiotemporal patterning of somite formation during normal development as well as the periodic abnormalities produced by heat shock treatment. We also relate the model to recent molecular data on the process of somite formation. (C) 2000 Academic Press.