Data supporting various dose-response relationships in chemical carcinogenesis are summarized. General principles are derived to explain the relationships between exposure dose, DNA adduct level, induction of genetic changes, and tumor incidence. Some mechanistic aspects of epigenetic carcinogens (stimulation of cell division and maldifferentiation) are analyzed in a similar way. In a homogeneous population, non-linearities are frequent. They are due to phenomena of induction or saturation of enzymatic activities and to the multi-step nature of carcinogenesis: if a carcinogen accelerates more than one step, the superposition of the dose-response curves for the individual steps can result in an exponential relationship. A fourth power of the dose was the maximum seen in animals (formaldehyde). At the lowest dose levels, a proportionality between dose and tumor induction is postulated independent of the mechanism of action if the carcinogen accelerates the endogenous process responsible for spontaneous tumor formation. Low-dose thresholds are expected only for situations where the carcinogen acts in a way that has no endogenous counterpart. Epidemlological studies in humans show linear dose-response curves in all but two investigations. The difference from the strongly non-linear slopes seen in animal studies could be due to the heterogeneity of the human population: if the individual sensitivity to a carcinogen is governed by a large number of genetic and life-style factors, the non-linearities will tend to cancel each other out and the dose-response curve becomes ‘quasi-linear'