Foulds introduced six rules of tumor progression based on his observations of spontaneous mammary cancer in mice and generalized them to all forms of neoplasia [Foulds, L. (1954) Cancer Res. 14, 327-339 and Foulds, L. (1969) Neoplastic Development (Academic, New York), Vol. 1, preface and pp. 72-74.] Rules III, IV, and V are considered controversial, and research in animals seems inadequate to resolve the controversies. A subline of NIH 3T3 cells undergoes progressive transformation to produce foci of increasing population density when repeatedly constrained by sequential rounds of growth to and maintenance at confluence. Analysis of the results provides a cellular basis for rules III, IV, and V. Rule III states that progression is independent of the growth of the tumor and occurs in tumors that are arrested. Cell culture shows that progression is actually favored by constraint of growth, a result inconsistent with a major role for point mutations in progression. Indeed, there is a suggestion that the transformation may arise from chromatin changes preceding apoptosis. Rule IV states that progression can be gradual or abrupt but the latter conclusion has been frequently criticized. Cell culture exhibits both forms of progression but, in particular, eliminates the doubt about the abrupt form. Rule V, which is in a sense an extension of rule IV, states that progression follows one of alternative paths of development. The results in culture indicate that every independent transforming event gives rise to foci of unique morphology. Thus, even for the single characteristic of transformed focus morphology, many alternative paths to neoplasia are available to cells. In addition to clarifying the rules of progression, a method is described for pinpointing the time of the occurrence of events that are only expressed as dense foci after a variable lag time. The results in culture reinforce Foulds' conclusion that neoplastic development is primarily an epigenetically driven process and identify some of the cellular interactions that underlie that process.