This thesis describes the gravity interpretation of Bahia State, Brazil, which comprises the northern Sao Francisco craton, the Upper Proterozoic fold belts and the basins adjacent to the continental margin. The study centres on the isostatic analysis of the region and on the interpretation of large and high amplitude negative anomalies which occur over the Precambrian and the sedimentary basins. The isostatic analysis of the northern Sao Francisco craton was carried out using the isostatic response function technique. Taking into account subsurface loads, an elastic plate with a minimum effective thickness of 20-40 km explains the observed isostatic response function. The subsurface loads are (l) a slight thickening of the crust under the Espinhaco Fold System and (2) five to ten kilometres of low density rocks in the upper crust. A large and high amplitude ( - 50 mGal ) negative anomaly of shallow origin, centred near the western border of the Paramirim complex and parallel to the Espinhaco fold belt, is interpreted as caused by a large and mainly unexposed granite batholith. The granite substantially underlies the fold belt and extends towards the centre of the Paramirim complex. The minimum density contrast between the granite and the country rocks is estimated to be -0.06 g cm(^-3). The thickness of the granite is 8 to 13 km for density contrasts of -0.15 g cm(^-3) to -0.10 g cm(^-3). A series of high amplitude negative anomalies (50 to 100 rrGal), without flanking positive anomalies, characterizes the onshore Reconcavo, Tucano and Jatoba basins, which were ail formed in connection with the South Atlantic opening. The gravity interpretation indicates up to 7 km of sediments infilling these basins and no significant Mo ho upwarp beneath. In contrast, the gravity anomalies over the offshore Jacuipe and Sergipe-Alagoas basins are explained by a thick accumulation of sediments on a strongly attenuated crust. The onshore basins show short-lived subsidence ( < 25 Ma) with little, if any thermal subsidence. Syn-rift and post-rift (thermal) sedimentation is observed only in the continental margin basins. A mechanism in which upper crustal extension in one region (onshore basins) is compensated and balanced against lower extension in another region (offshore basins), through a detachment fault, may explain the way these basins formed.