Irradiation from internally deposited radionuclides induces malignant tumors. Ingested long-lived radionuclides accumulate in specific organs that are irradiated throughout life. To elucidate why the development of malignant tumors requires long-term internal exposure, of the order of decades, despite the fact that irradiation is continuous over this period, we analyzed intrahepatic cholangiocarcinoma in Thorotrast patients (Th-ICC). Autoradiography showed that the density of alpha-particle tracks was 50 times more concentrated than would be expected if Thorotrast were evenly distributed throughout the liver. The age-incidence curves revealed that while the incidence of hepatobiliary cancer in Japan increased in proportion to the 7th power of age, that of Th-ICC increased to the 6th power. Internal radiation significantly increased the randomness of hepatocyte distribution but not the density. Three major factors are considered to be responsible for the long incubation time: the uneven distribution of radionuclides, the limited range of radiation, and the movement of tumor precursor cells. Target cells susceptible to malignant transformation may undergo one event and may then migrate outside of the range of alpha particles, thereby avoiding immediate induction of successive additional events that would lead to cell death or neoplastic changes.