We have used biostratigraphic data from deep exploration wells to determine the tectonic subsidence history of the Somaliland (northwestern Somalia)-Yemen conjugate margin, a poorly known margin in the central part of the Gulf of Aden. Bathymetry and magnetic anomaly data suggest the Gulf of Aden is a young feature that formed following the rifting apart and breakup of the African and Arabian plates ~32 Ma. Our tectonic subsidence data suggest, however, that the present-day Gulf of Aden developed on an earlier Mesozoic rift system. The oldest episode of rifting initiated at ~156 Ma and lasted for ~10 Ma and had a NW-SE trend. We interpret the rift as a late stage event associated with the breakup of Gondwana and the separation of Africa and Madagascar. At ~80 Ma, there is evidence of an intermediate rift event which correlates with a rapid increase in spreading rate on the ridges separating the African and Indian and African and Antarctica plates and a contemporaneous slowing down of Africa's plate motion. The combined effect of all three rifting events has been to thin the crust and upper mantle by up to a factor of 2. The amount of thinning deduced from the wells is in accord with the crustal structure inferred from available seismic refraction data and process-oriented gravity and flexure modeling. The margin is asymmetric with a steeper gradient in the Moho on the Yemen side than the Somaliland side. The main discrepancy is on the Yemen side where the gravity-derived Moho is 10 km deeper than the well-derived Moho. We attribute the discrepancy to the addition of material at the base of the crust since rifting, possibly magma sourced from the Afar plume.