In front of examples of different types of exposures to ionizing radiation, the epidemiologists have the opportunity to verify if the dose response relationship that has been observed in one precisely defined situation is also "true", when being confronted to other populations, with different backgrounds and different ways of exposure over time. The challenge in future years will be to get better information on populations exposed to low chronic exposure protracted over a large number of years. In this paper, the lessons of two situations will be confronted, populations exposed to accidnetal exposure, like survivors of Hiroshima and Nagasaki and those with a dally exposure to alpha particles by inhaling radon gas. In each of these situations the way of human exposures is different, whole body exposure over several seconds in Hiroshima and Nagasaki ans a dally local irradiation to the lung in the case of uranium miners. The situation of the follow-up of populations after Chernobyl is briefly discussed, current results being still unable to support a clear dose-response relationship.