In the early 1960s, the US Geological Survey began routinely analysing river water samples for tritium concentrations at locations within the Mississippi River basin. The sites included the main stem of the Mississippi River (at Luling Ferry, Louisiana), and three of its major tributaries, the Ohio River (at Markland Dam, Kentucky), the upper Missouri River (at Nebraska City, Nebraska) and the Arkansas River (near Van Buren, Arkansas). The measurements cover the period during the peak of the bomb-produced tritium transient when tritium concentrations in precipitation rose above natural levels by two to three orders of magnitude. Using measurements of tritium concentrations in precipitation, a tritium input function was established for the river basins above the Ohio River, Missouri River and Arkansas River sampling locations. Owing to the extent of the basin above the Luling Ferry site, no input function was developed for that location. The input functions for the Ohio and Missouri Rivers were then used in a two-component mixing model to estimate residence times of water within these two basins. (The Arkansas River was not modelled because of extremely large yearly variations in flow during the peak of the tritium transient.) The two components used were: (i) recent precipitation (prompt outflow) and (ii) waters derived from the long-term groundwater reservoir of the basin. The tritium concentration of the second component is a function of the atmospheric input and the residence times of the groundwaters within the basin. Using yearly time periods, the parameters of the model were varied until a best fit was obtained between modelled and measured tritium data. The results from the model indicate that about 40% of the flow in the Ohio River was from prompt outflow, as compared with 10% for the Missouri River. Mean residence times of 10 years were calculated for the groundwater component of the Ohio River versus 4 years for the Missouri River. The mass flux of tritium through the Mississippi Basin and its tributaries was calculated during the years that tritium measurements were made. The cumulative fluxes, calculated in grams of 3H were: (i) 160 g for the Ohio (1961–1986), (ii) 98 g for the upper Missouri (1963–1997), (iii) 30 g for the Arkansas (1961–1997) and (iv) 780 g for the Mississippi (1961–1997). Copyright © 2004 John Wiley & Sons, Ltd.