Oncogenesis is the result of accumulation of specific gene mutations. Two classes of specific cancer mutations are distinguished: namely those affecting anti-oncogenes and those in which oncogenes are involved. Anti-oncogenes are thought to regulate normal growth by encoding proteins that inhibit the expression of the oncogenes. This is in line with the observation that tumor cells are often homozygous for a defect in an anti-oncogene, as this will allow the expression of an oncogene. In this paper we attempt to calculate the number of anti-oncogenes involved in the genesis of a malignant tumour cell. These calculations were initially performed using a simplified model for oncogenesis and later applied to more complicated situations. These calculations indicate that usually four mutations in anti-oncogenes are required for oncogenesis in adults. This is in contradiction to the well-known 2-hit model of oncogenesis of Knudson which predicts about 10(9) times more de novo arising tumour cells than are observed in reality. Oncogenesis is only observed in proliferating cells. Cell proliferation and growth kinetics in various organs differ greatly. Therefore the time of oncogenesis and tumour manifestation also varies in the different organs. In organs that develop in early life (e.g. retina and neurons of the brain) mitotic activity ceases soon after birth. Consequently neural and retinal tumours emerge only early in life. In contrast, the main development of the female breast occurs after puberty, and the earliest breast tumours will become apparent in young adults. The four recessive mutations in anti-oncogenes required for oncogenesis imply that probably recessive mutations are involved in two loci. It is clear that an inherited mutation in an anti-oncogene at a particular locus causes different tumour types depending on the various organs in which the tumours arise. Comparison of (a) results of calculations about the number of malignant neuroendocrine tumour cells that arise in a pancreatic islet of a patient with inherited MEN1-syndrome with (b) the pathological anatomy of such a patient, suggests that a cell with two or three oncogenic mutations has a growth advantage over normal cells. This leads to cell proliferation in a premalignant lesion until the set of four oncogenic mutations is complete. The clinically premalignant lesions have a maximal mean diameter of about 0.4 cm when the first true malignant tumour cell develops, and the pathologist will probably note malignancy when the lesion has the size of 1-2 cm.(ABSTRACT TRUNCATED AT 400 WORDS)