Between 1986 and 1990, several hundred thousand workers, called "liquidators" or "clean-up workers," took part in decontamination and recovery activities within the 30-km zone around the Chernobyl nuclear power plant in Ukraine, where a major accident occurred in April 1986. The Chernobyl liquidators were mainly exposed to external ionizing radiation levels that depended primarily on their work locations and the time after the accident when the work was performed. Because individual doses were often monitored inadequately or were not monitored at all for the majority of liquidators, a new method of photon (i.e., gamma and x rays) dose assessment, called "RADRUE" (Realistic Analytical Dose Reconstruction with Uncertainty Estimation), was developed to obtain unbiased and reasonably accurate estimates for use in three epidemiologic studies of hematological malignancies and thyroid cancer among liquidators. The RADRUE program implements a time-and-motion dose-reconstruction method that is flexible and conceptually easy to understand. It includes a large exposure rate database and interpolation and extrapolation techniques to calculate exposure rates at places where liquidators lived and worked within approximately 70 km of the destroyed reactor. The RADRUE technique relies on data collected from subjects' interviews conducted by trained interviewers, and on expert dosimetrists to interpret the information and provide supplementary information, when necessary, based upon their own Chernobyl experience. The RADRUE technique was used to estimate doses from external irradiation, as well as uncertainties, to the bone marrow for 929 subjects and to the thyroid gland for 530 subjects enrolled in epidemiologic studies. Individual bone marrow dose estimates were found to range from less than one muGy to 3,300 mGy, with an arithmetic mean of 71 mGy. Individual thyroid dose estimates were lower and ranged from 20 muGy to 507 mGy, with an arithmetic mean of 29 mGy. The uncertainties, expressed in terms of geometric standard deviations, ranged from 1.1 to 5.8, with an arithmetic mean of 1.9.