Tumor induction data in the mouse skin initiation-promotion system were found to be consistent with a quadratic function where the coefficient of the linear term depended on the dose of the promoter. The model implies that the existence of promoters may be more important at low doses of the carcinogen than at high doses where most testing is performed. Experiments are described showing that the initiating effect of carcinogenic chemicals, such as benzo(a)pyrene, 7,12-dimethyl-benz(a)anthracene, nitroquinoline oxide and beta-propiolactone, accumulates in a linear, irreversible manner at low doses. Even when 7,12-dimethylbenz(a)anthracene was applied intragastrically to pregnant females, initiating activity was found in the skins of exposed offspring about in proportion to dose applied and number of cells at risk. The initiated cells essentially represent a potential for cancer that has a high probability for expression in the presence of a promoter. Risk then can be interpreted in terms of the accumulated dose of initiator which alone presents a small risk of cancer. However, a promoter may substantially expand the overall risk, possibly by clonally expanding the initiated cells. Promotion needs to be sustained since there is a reduction of cancer risk if promotion is ended early. Some tissues, such as mouse bladder, may be intrinsically promoted more than others so that comparisons between tissues and between species are best made when the combination of intrinsic promotion and response to extrinsic promotion are comparable.