Long-range atmospheric transport of radionuclides from the Chernobyl accident is modelled as an Eulerian diffusion process. From observations of the gross deposition pattern of particulate radiocaesium an effective long-range Eddy diffusivity K of the order of 10(6) m(2) s(-1) is inferred. A corresponding effective deposition length for caesium, R-Cs, defined las the effective distance from Chernobyl to where the aerosols have been deposited, is found to be R-Cs approximate to 1000 km. From the observations of the regional variability of the Chernobyl fallout a simple probabilistic assessment method is proposed for the long-range radiological consequences of nuclear accidents. (C) 1999 Elsevier Science Ltd. All rights reserved.