Conservational models, like simple shear, pure shear or polyphase models that exclude exchanges between the lower continental crust and upper mantle, are usually proposed to explain the lithospheric stretching and consequent crustal thinning of passive continental margins. These models need large amounts of horizontal movement, and have, therefore, important implications for plate kinematic reconstructions and intraplate deformation. In this paper we propose to show these implications in the Central Segment of the South Atlantic Ocean. In the Angola–Brazilian system, these models imply about 240 km of horizontal movement. This movement can be compensated by two end-member mechanisms: (1) an intraplate deformation located in Africa; and (2) an intraplate deformation located in South America. We detail for each solution the strong geological and geodynamical implications, and discuss the consequences for the genesis of passive continental margins.