Mathematical modeling of risk of lung cancer upon smoking cessation suggests increasing risk, whereas the facts show decreasing mortality. This discordance is resolved by taking into account the mechanistically distinct steps in chemical carcinogenesis: (1) neoplastic conversion hygenotoxic carcinogens and (2) neoplastic growth and development by agents with epigenetic and promoting effects. Tobacco smoke contains relatively small amounts of several types of genotoxic carcinogens, the effect of which is considerably and vitally enhanced by nongenotoxic promoting factors. Upon smoking cessation, the effect of the second type of agent is abruptly eliminated. Therefore, any preneoplastic lesions remain static or regress, whereas in the continuing smoker they progress. These sequences also apply, with different chemicals involved, in nutritional carcinogenesis. (Epidemiology 1990;1:314–317)