[en] Samples of atmospheric dust and rainwater have been collected from the United Kingdom and elsewhere. Results are presented of analyses of these samples for various fission products and certain other radionuclides. The average concentrations of long-lived fission products in air and rain in the United Kingdom in 1977 were about double those in 1976 and about 2% of the maximum which was reached in 1963-64. A similar rise occurred between 1973 and 1974. Despite such fluctuations the general trend is of slowly decreasing concentrations. Plutonium concentrations in air at Chilton are discussed for the years 1954-1977 and generally follow the pattern of long-lived fission products. Barium-140 and iodine-131 indicative of a recent atmospheric test were detected in air and rain in the United Kingdom after the low yield Chinese explosion of 17 September 1977. Iodine-131 ceased to be detectable by mid-October and barium-140 by December 1977. In the southern hemisphere the mean concentration of caesium-137 in air in 1977 was about two-thirds that in 1976. An estimate is made of the worldwide deposit of caesium-137 and strontium-90 which, in 1976, was the lowest since measurements were started in 1955. The gamma and beta-ray dose rates from fallout at Chilton are estimated from the observed deposition. Measurements of short-lived fission products in air and rain are given in an Appendix. (author)