The Brazilian and West African Equatorial margins comprise an unique example of a transform margin, characterized by a series of on-and offshore Mesozoic-Cenozoic basins, distributed over 2,200 km along the South Atlantic. Although a multi-stage stretching process evolved throughout the Aptian-Cenomanian, an almost instantaneous Aptian stage was responsible for a widespread fracturing of the Equatorial Atlantic. Conventional extensional processes can not explain the kinematics and rift geometry of the Equatorial South Atlantic basins. Accepted pure-shear or simple-shear rift mechanisms, typical of divergent margins, cannot be promptly used in basins generated as a response to major transform motions along a continental-scale plate boundary. The commonly accepted causal processes for rifting, such as passive/active or diffuse/discrete rifting, can not accommodate the South Atlantic Equatorial data set. Even though shearing signatures and pull-apart features are easily recognized throughout the margin, their magnitude and basin architecture varies significantly as a function of the distance from the main transform faults. These factors resulted in significant differences in thermal evolution, tectonic subsidence, facies distribution and uplift history. The tectonic evolution of the sedimentary basins along the Equatorial Atlantic is better understood by considering three stages: pre, syn and posttransform movements. These are related to kinematic and dynamic controls provided by the emplacement of fractured swells as proto mid ocean ridges, followed by the creation of oceanic crust and the onset of transform shearing between Africa and Brazil.