Recent observations and models of continental rifting in magma‐poor environments have led to the concept of multiphase stages of lithospheric extension. In these concepts it is shown that extreme crustal thinning of the crust predates exhumation of lower crustal and subcontinental mantle rocks during final rifting. The Bay of Biscay is a V‐shaped ocean basin that opened in Aptian‐Albian time. In front of this propagating ocean, several rift basins formed that show evidence for extreme crustal thinning and locally also mantle exhumation (the Parentis, Arzacq‐Mauleon, and Cantabrian basins). In this paper we propose, based on geological and geophysical observations and using numerical modeling, a model that can explain the extreme crustal thinning observed in the Arzacq‐Mauléon and Parentis basins. Our results show that rifting in the Bay of Biscay was initiated by distributed oblique stretching (latest Jurassic to Early Aptian) before it underwent an more orthogonal asymmetric thinning and exhumation phase from Late Aptian to Albian time. These last two stages of deformation are similar to those observed in orthogonal rift systems. We show that thinning is accomplished by the formation of a semibrittle shear zone that allows for the transfer of middle to lower crustal material from the side of the rift collocated with the hanging wall to the side of the rift collocated with the footwall of the detachment system. The main difference with an orthogonal rift system appears to be generated by the formation of flower structures during the distributed oblique phase and the capacity of localizing the deformation in the subsequent stages. These oblique slip faults form very steep normal faults that induce the development of strongly localized, compartmentalized, and asymmetric rift basins. In the case of the Parentis and Arzacq‐Mauleon basins, these strike‐slip faults separate upper plate sag basins to the north from lower plate sag basins to the south. While the northern sag basins do not show any evidence for exhumation, the southern ones are more complex and floored by detachment faults, as indicated by the occurrence of syntectonic and posttectonic sediments onlapping directly onto exhumed lower crustal and mantle rocks.