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Under an IAEA's Co-ordinated Research Project "Worldwide Marine Radioactivity Studies (WOMARS)" 90Sr, 137Cs and (239,240)Pu concentration surface water time series in the Pacific and Indian Oceans have been investigated. The Pacific and Indian Oceans were divided into 17 latitudinal boxes according to ocean circulation, global fallout patterns and the location of nuclear weapons test sites. The present levels and time trends in radionuclide concentrations in surface water for each box were studied and the corresponding effective half-lives were estimated. For the year 2000, the estimated average 90Sr, 137Cs and (239,240)Pu concentrations in surface waters of the Pacific and Indian Oceans varied from 0.1 to 1.5 mBq/L, 0.1 to 2.8 mBq/L, and 0.1 to 5.2 microBq/L, respectively. The mean effective half-lives for 90Sr and 137Cs in surface water were 12+/-1 years for the North, 20+/-1 years for the South and 21+/-2 years for the Equatorial Pacific. For (239,240)Pu the corresponding mean effective half-lives were 7+/-1 years for the North, 12+/-4 years for the South and 10+/-2 years for the Equatorial Pacific. For the Indian Ocean the mean effective half-lives of 137Cs and (239,240)Pu were 21+/-2 years and 9+/-1 years, respectively. There is evidence that fallout removal rates before 1970 were faster than those observed during recent decades. The estimated surface water concentrations of 90Sr, 137Cs and (239,240)Pu in latitudinal belts of the Pacific and Indian Oceans for the year 2000 may be used as the average levels so that any new contribution from nuclear facilities, nuclear weapons test sites, radioactive waste dumping sites and from possible nuclear accidents can be identified.