Ramp-syncline basins (RSBs) are characterized by asymmetric depocentres formed by translation above salt detachments with basal steps. Recognition of these minibasins allows quantification of the magnitude and rates of overburden translation above a deforming salt layer. 3D seismic data from the São Paulo Plateau, Santos Basin, Brazil image a series of RSBs formed above thick salt, and distributed above and/or basinward of pronounced base-salt steps. The RSBs are composed of landward-dipping and gently folded sigmoidal strata, recording 28–32 km of SE-directed translation during the Late Cretaceous and Paleocene, at an average rate of 0.8–0.9 mm/year. We present several examples of RSBs, in addition to results from numerical forward models, to analyse the 3D kinematics of RSBs and their interaction with base-salt structures. The RSBs form not only by translation above basinward-dipping ramps, but also over landward-dipping ramps. Translation over stepped ramps generates stacked RSBs. Thickness maps show translation is higher at the centre of RSBs and that depocentres become progressively more affected by diapirism as they evolve. This study presents the first analysis of the 3D kinematics of ramp-syncline basins, and the first documentation of their occurrence above thick salt in the Santos Basin, Brazil. It applies realistic numerical models that treat the detachment as a volume of viscous material, improving our understanding of these systems. RSBs are important to understand slope and deep-basin tectono-stratigraphic architecture of supra-salt units and can also guide the identification of pre-salt structures, thus contributing to the exploration of salt basins.