International audience The eastern Alboran basin and its transition to the Algerian basin is a key area in the Mediterranean realm where controversial kinematic and geodynamical models are proposed. Models imply striking differences regarding the nature of the crust, the prevalence of brittle faulting and ductile shear, the origin of magmatism, the style of Miocene deformation and the driving mechanisms of the Alboran plate kinematics. Combining a new chronostratigraphic chart of the Alboran and Algerian basins based on the Habibas (HBB-1) core drill, deep seismic sections striking WSW-ENE and SSE-NNW, and potential field data, we re-assess the tectonic evolution that controlled the sedimentation and basement deformation of the westernmost limit of the Algerian basin and its transition with the Alboran domain. A WSW-directed extensional tectonic phase has shaped a stretched continental crust with typical tilted blocks along ∼100 km from Burdigalian to Tortonian times, which is assumed to result from the WSW-directed migration of the Alboran block driven by a narrow slab rollback. In the Algerian basin, this event was followed by the emplacement of an oceanic-type crust. Potential field signatures of the deep basin as well as geometrical correlations with onland outcrops of inner zones suggest a minimum WSW-directed displacement of the Alboran terrane of ∼200 km. At the southern foot of the Algerian basin, the continent-ocean transition is sharp and may result from the westward propagation of a slab tear at depth, forming two segments of STEP (Subduction-Transform Edge Propagator) margins. Our results support models of intense shear tractions at the base of an overriding plate governed by slab rollback-induced mantle flow. Finally, Messinian salt tectonics affected overlying deposits until today. A late Tortonian to Quaternary dominantly transpressive tectonic episode linked to the Africa-Iberia convergence post-dates previous events, deforming the whole margin.