Under the assumption that a malignant tumor develops through a sequence of steps (normal cells->initiated cells/foci->nodules->tumors) two classes of mathematical models of carcinogenesis that have a potential to be used for cancer dose-response modeling are discussed. The two classes of models considered are (1) a general version of the two-stage model by Moolgavkar and colleagues, henceforth called the MVK model, and (2) a clone process model derived from Tucker. These two classes of models incorporate essentially the same biological information but in different ways and offer a conceptual contrast between the two differing approaches. The objectives of the paper are to (1) highlight issues and problems that arise in using biologically based dose-response models to predict cancer risk and (2) discuss how parameters in the models could be estimated using auxiliary information.