During the Algerian-French SPIRAL survey aimed at investigating the deep structure of the Algerian margin and basin, two coincident wide-angle and reflection seismic profiles were acquired in central Algeria, offshore Greater Kabylia, together with gravimetric, bathymetric and magnetic data. This ~260 km-long offshore-onshore profile spans the Balearic basin, the central Algerian margin and the Greater Kabylia block up to the southward limit of the internal zones onshore. Results are obtained from modeling and interpretation of the combined data sets.The Algerian basin offshore Greater Kabylia is floored by a thin oceanic crust (~4 km) with P-wave velocities ranging between 5.2 and 6.8 km/s. In the northern Hannibal High region, the atypical 3-layer crustal structure is interpreted as volcanic products stacked over a thin crust similar to that bordering the margin and related to Miocene post-accretion volcanism. These results support a two-step back-arc opening of the west-Algerian basin, comprising oceanic crust accretion during the first southward stage, and a magmatic and probably tectonic reworking of this young oceanic basement during the second, westward, opening phase. The structure of the central Algerian margin is that of a narrow (~70 km), magma-poor rifted margin, with a wider zone of distal thinned continental crust than on the other margin segments. There is no evidence for mantle exhumation in the sharp ocean-continent transition, but transcurrent movements during the second opening phase may have changed its initial geometry. The Plio-Quaternary inversion of the margin related to ongoing convergence between Africa and Eurasia is expressed by a blind thrust system under the margin rising toward the surface at the slope toe, and by an isostatic disequilibrium resulting from opposite flexures of two plates decoupled at the continental slope. This disequilibrium is likely responsible for the peculiar asymmetrical shape of the crustal neck that may thus be a characteristic feature of inverted rifted margins.