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SUMMARY We use a thin-shell approximation for the lithosphere to model the neotectonics of the Gulf of Cadiz, SW Iberia margin and the westernmost Mediterranean, in the eastern segment of the Azores-Gibraltar plate boundary. In relation to previous neotectonic models in the region, we utilize a better constrained structural map offshore, and the recent GPS measurements over NW Africa and Iberia have been taken into account, together with the seismic strain rate and stress data, to evaluate alternative geodynamic settings proposed for the region. We show that by assuming a relatively simple, two-plate tectonic framework, where Nubia and Eurasia converge NW-SE to WNW-ESE at a rate of 4.5-6 mm yr−1, the models correctly predict the amount of shortening and wrenching between northern Algeria-Morocco and southern Spain and between NW Morocco and SW Iberia, as estimated from both GPS data and geological constraints. The consistency between modelled and observed velocities in the vicinity of Gibraltar and NW Morocco indicates that forcing by slab sinking beneath Gibraltar is not required to reproduce current horizontal deformation in these areas. In the Gulf of Cadiz and SW Iberia, the modelling results support a diffuse Nubia-Eurasia Plate boundary, where the convergence is accommodated along NNE-SSW to NE-SW and ENE-WSW thrust faults and WNW-ESE right-lateral strike-slip faults, over an area >200 km wide, in good general agreement with the distribution of the seismic strain rate and associated faulting mechanisms. The modelling results are robust to regional uncertainties in the structure of the lithosphere and have important implications for the earthquake and tsunami hazard of Portugal, SW Spain and Morocco. We predict maximum, long-term average fault slip rates between 1-2 mm yr−1, that is, less than 50 per cent the average plate relative movement, suggesting very long return periods for high-magnitude ( Mw > 8) earthquakes on individual structures. [ABSTRACT FROM AUTHOR]