We investigated the process of induction of preneoplastic cells positive for glutathione S-transferase P-form (GST-P) in the rat liver. AAF (2-Acetylaminofluorene) mixed with normal rat chow at high concentration (0.04%) induced 517 000 ± 86 000 GST-P+ single hepatocytes/g liver after 2 weeks followed by induction of a few foci and nodules after 4–6 weeks. Overproduction of GST-P+ single hepatocytes was dose- and time-dependent, and the induction kinetics were typical of first-order consecutive reaction, by which induction of the positive cells was nongenetic. Quantitative analysis indicated that the estimated numbers of cells in foci and nodules at 4–6 weeks after exposure to AAF ranged from 2.7 × 104 (214.7) to 3.6 × 106 (221.7) cells, and 2.0 × 104 (214.3) to 2.7 × 106 (221.4) cells, respectively, when analyzed by using two equations. According to the initiated cell theory of Farber, foci and nodules are formed through sequential cell division of 14 to 21-times or more within a short time period. The rapid growth exceeded the rate of cell division, indicating that the growth of preneoplastic cells is based on a nonclonal penetration mechanism. (Cancer Sci, doi: 10.1111/j.1349-7006.2012.02325.x, 2012)