Environmental radiocaesium (137Cs) originates primarily from two sources, atmospheric nuclear weapons testing, and the Chernobyl accident. It has not, to our knowledge, previously been possible statistically to compare changes in the environmental mobility of 137Cs from these two sources since the weapons test fallout varied in a complex manner over a number of years. A novel technique is presented for curve-fitting measurements with a time-dependent input function such as that for weapons test fallout. Different models were fitted to measurements of both pre- and post-Chernobyl 137Cs activity concentrations in five major Finnish rivers. It was shown that there was no significant difference in the temporal changes in 137Cs mobility from these two sources during the years after fallout. Transport parameters derived from weapons test measurements gave good predictions of the long-term contamination of these rivers by Chernobyl fallout. Changes in 137Cs activity concentrations in rivers after Chernobyl have previously been shown to decline as a result of slow sorption to clay minerals in catchment soils. It is shown that weapons test fallout also exhibited this slow decline over time. Rates of decline in 137Cs activity concentrations 10 years after fallout correspond to effective ecological half-lives (Teff) in the range 10-30 years. Removal of activity from the catchment was found to have no significant effect on the long-term decline in 137Cs activity concentrations in these rivers.