Geostrophic transports of the western boundary currents at the Brazil/Malvinas Confluence in the South Atlantic Ocean are estimated from the data set of the Confluence 3 cruise (February 1990) with a nonlinear inverse model which takes into consideration density, current meter and wind data, and dynamical (planetary vorticity, Ekman, mass conservation) constraints. Inversions are carried out with two initial different levels of no motion at 1500 m (Case A) and at 3000 m (Case B). Consistencies of the water volume transports provided by both inversions are analyzed and compared to previous estimates. Current meter constraints are applied in the Malvinas Current region where a total transport of 45 +/- 7 Sv (1 Sv = 10(6) m(3) s(-1)) is given by both inversions. Within the Brazil Current region, discrepancies between both inversions appear. Case A provides a total transport of 30 +/- 7 Sv while case B gives a total transport of 56 +/- 8 Sv. In the first two layers (0-1000 m; 1000-2000 m), case B (53 Sv) gives larger transport than case A (32 Sv). North of the Confluence and at the North Atlantic level, water is found to flow northward in case A at a rate of 3.4 +/- 2 Sv and southward in case B at a rate of 3 +/- 3 Sv. Case B results are more in agreement with our present knowledge of water mass circulation in the Confluence region than case A results. Eastward transports at the Brazil-Malvinas Confluence are estimated to be 20 +/- 7 Sv and 30 +/- 7 Sv for cases A and B, respectively. Compared to the total transports of the Brazil and Malvinas Currents, these estimates suggest that most of the water supplied to the Confluence area recirculates within the Brazil Current and the Malvinas Current regions.