Colorectal cancer is initiated in colonic crypts. A succession of genetic mutations or epigenetic changes can lead to homeostasis in the crypt being overcome, and subsequent unbounded growth. We consider the dynamics of a single colorectal crypt by using a compartmental approach [Tomlinson IPM, Bodmer WF (1995) Proc Natl Acad Sci USA 92:11130 -11134], which accounts for populations of stem cells, differentiated cells, and transit cells. That original model made the simplifying assumptions that each cell population divides synchronously, but we relax these assumptions by adopting an age-structured approach that models asynchronous cell division, and by using a continuum model. We discuss two mechanisms that could regulate the growth of cell numbers and maintain the equilibrium that is normally observed in the crypt. The first will always maintain an equilibrium for all parameter values, whereas the second can allow unbounded proliferation if the net per capita growth rates are large enough. Results show that an increase in cell renewal, which is equivalent to a failure of programmed cell death or of differentiation, can lead to the growth of cancers. The second model can be used to explain the long lag phases in tumor growth, during which new, higher equilibria are reached, before unlimited growth in cell numbers ensues.age-structure ͉ feedback ͉ mutations ͉ structural stability T he large intestine is one of the most frequent sites of carcinogenesis due, at least in part, to its continual selfrenewal and the large numbers of daily cell divisions (1). There are millions of invaginations in the lining of the colon, called crypts, and it is widely believed that colorectal cancer is initiated when mutations or relatively stable epigenetic changes occur in the single layer of epithelial cells that line the crypt. Consequently, much work has been directed toward understanding the mechanisms involved in the dynamics of the cells in healthy and neoplastic (abnormally growing) crypts.Stem cells are believed to reside near the bottom of the colorectal crypt (2), and these are capable of producing a variety of cell types that are required for tissue renewal and regeneration after injury (3). The stem cells divide to produce transit cells that migrate up the crypt wall toward the luminal surface. As the cells proceed up the crypt they differentiate into colonocytes, enteroendocrine cells, and Goblet cells (1). Once at the top, the cells either undergo apoptosis and͞or are shed into the lumen and transported away (4, 5).In the murine small intestine, the journey of the cells from the base of the crypt to its apex has been estimated to take between 2 and 3 days (6), and all the cells in the crypt, apart from the stem cells, will be renewed over this period. The stem cells are assumed to have a cycle time of between 12 and 32 h with an average of 24 h (7, 8). The transit cell population has an estimated cycle time of Ϸ11-12 h (4, 9).The crypt is homeostatic with an equilibrium maintained between cell proliferation and cell los...