The Parentis and Arzacq-Mauleon basins located in front of the V-shaped oceanic propagator in the Bay of Biscay present evidence for extreme crustal thinning. In this paper we investigate the 3D structure of these rift basins, based on field observations and the interpretation of seismic data. We compare these results with those obtained from two different and independent inversion methods: first a 3D gravity inversion and second the standard Euler deconvolution.;For the Mauleon Basin our results show that the positive gravimetric anomaly identified above its southern margin is the consequence of two shallower high density bodies that are separated by the Pamplona fault and a deeper high density body. The high density bodies can be explained by the presence of mid-crustal and mantle rocks that were exhumed or uplifted at shallower depth during Early Cretaceous rifting before they were reworked and integrated to the Pyrenean chain during compression phase. Also, during this reactivation phase, some slices of the exhumed mid-crustal and mantle rocks were sheared off and were integrated in the present-day thrust belt in the Mauleon basin. For the Parentis Basin we can demonstrate, based on seismic data and gravimetric inversion methods, a decrease in extension from west to east, which is compatible with the V-shape geometry of the overall basin. Along strike, a change in the fault geometry from downward concave top-basement detachment faults to upward concave high-angle faults can be observed eastwards, i.e. towards the termination of the basin. A key structure, controlling the evolution of the Parentis Basin, is the east-west trending Ibis fault. We interpret this fault to have initially formed as a strike slip fault before it was reactivated during later crustal thinning. At present, it forms the limit between an upper plate sag basin to the north and a lower plate sag basin, floored at least locally by a top-basement detachment faults to the south. The strong asymmetry of the basin is supported by the shape of the basin and the results of standard Euler deconvolution.