The Ligurian basin, western Mediterranean Sea, has opened from late Oligocene to early Miocene times, behind the Apulian subduction zone and partly within the western Alpine belt. We analyze the deep structures of the basin and its conjugate margins in order to describe the tectonic styles of opening and to investigate the possible contributions of forces responsible for the basin formation, especially the pulling force induced by the retreating subduction hinge and the gravitational body force from the Alpine wedge. To undertake this analysis, we combine new multichannel seismic reflection data (Malis cruise, 1995) with other geophysical data (previous multichannel and monochannel seismic sections, magnetic anomalies) and constrain them by geological sampling from two recent cruises (dredges from Marco cruise, 1995, and submersible dives from Cylice cruise, 1997). From an analysis of basement morphology and seismic facies, we refine the extent of the different domains in the Ligurian Sea: (1) the continental thinned margins, with strong changes in width and structure along strike and on both sides of the ocean; (2) the transitional domain to the basin; and (3) a narrow, atypical oceanic domain. Margin structures are characterized by few tilted blocks along the narrow margins, where inherited structures seem to control synrift sedimentation and margin segmentation. On the NW Corsican margin, extension is distributed over more than 120 km, including offshore Alpine Corsica, and several oceanward faults sole on a relatively flat reflector. We interpret them as previous Alpine thrusts reactivated during rifting as normal faults soling on a normal ductile shear zone. Using correlations between magnetic data, seismic facies, and sampling, we propose a new map of the distribution of magmatism. The oceanic domain depicts narrow, isolated magnetic anomalies and is interpreted as tholeitic volcanics settled within an unroofed upper mantle, whereas calcalkaline volcanism appears to be discontinuous but massive and has jumped in space and time, from the beginning of rifting on the Ligurian margin (~30 Ma), toward the Corsican margin at the end of the Corsica-Sardinia block rotation (~16 Ma). This space and time shift reveals the importance of the rollback of the Apulian slab and of the migration of the Alpine-Apennines belt front toward the E-SE for driving basin formation. We also state that initial rheological conditions and inherited crustal fabric induce important changes in the styles of deformation observed along margins and between conjugate margins. In the NE Ligurian basin the prerift Alpine crustal thickening together with slow rollback velocity likely contribute to distribute strain across the whole NW Corsican margin, whereas farther south the inherited Hercynian structural pattern combined with a faster rollback of the subducting plate tend to focus the extension at the foot of the margin, up to the Sardinian rift which ends within the SW Corsican margin. Therefore the mode of opening and the margin structures mainly depend on the balance between intrinsic, inherited crustal heterogeneity (fabric and rheological changes) and external conditions imposed by rollback of the subducting lithosphere.