Several multistage models have been proposed to describe the process of carcinogenesis. The model attributed to Armitage and Doll (1954, Brit. J. Cancer 8, 1-12) assumes that a normal cell is transformed into a malignant cell by k greater than or equal to 1 fundamental biological events. The model usually attributed to Moolgavkar and colleagues (1979, Math. Biosci. 47, 54-77; 1981, J. Natl. Cancer Inst. 66, 1037-1052) assumes that carcinogenesis is a two-stage process, taking into account the ability of premalignant cells to proliferate. In this paper, we investigate our ability to distinguish between these models using animal carcinogenicity data. Three different approaches are considered: one based on actual tumor incidence data from National Toxicology Program experiments and two based on simulated data. The results show that both models will adequately fit most tumor incidence data. This implies that we must be cautious in accepting the biological basis of either of these models simply because it "fits the data." Suggestions for experimental designs and toxicological endpoints (other than tumor incidence) which might provide for better discrimination between models are given.