Abstract The paper examines aspects of the sedimentology and stratigraphy of rift basins that evolved in deep marine settings near the ocean-continent transition. It focuses on the applicability of a low-angle extensional detachment model developed in the Alps to the West Iberian margin, and on difficulties of objectively identifying syn-rift stratigraphic intervals in both areas. The paper examines evidence obtained from Ocean Drilling Program holes drilled in the Iberia Abyssal Plain. Despite the fact that all the holes were sited above highs in the acoustic basement and so did not penetrate a complete sedimentary record of rifting, they do provide some constraints on the age and mechanism of rifting. We suggest that published identifications of syn-rift intervals in distal basins off West Iberia and in the Southern Alps have not demonstrated, using objective criteria, the occurrence of syn-rift stratigraphic intervals. They have, therefore, probably overestimated the duration of rifting by as much as 20 Ma. The absence of syn-rift related stratal divergence towards fault footwalls may be due to resedimentation of syn-rift sediments towards basin centres, lack of significant hanging-wall rotation along flat detachment faults, or the syn-rift interval being too thin to resolve on seismic data. The syn-rift episode beneath the deep Galicia margin postdates Tithonian-Berriasian shallow-water carbonates, and predates Late Valanginian turbiditic sediments. Drilling results from the Iberia Abyssal Plain suggest a similar age because Tithonian siliciclastic mudrocks are overlain by Berriasian pelagic chalks. It seems likely that in both regions rifting lasted for <5 Ma, probably from late Berriasian to early Valanginian. At Site 1068 in the Iberia Abyssal Plain, the interpretation from seismic reflection data, of a low-angle detachment dipping about 10° west, was confirmed by drilling, which revealed sedimentary and tectonic breccias containing clasts of lower-crustal rocks overlying a fault zone below which occurs serpentinized periodotite showing a downward decrease in deformation. At least 20.5 km of displacement is interpreted to have occurred along this fault, but it is not accompanied by large-amplitude, rift-related topography. This paradox is resolved if the detachment developed as a deepening-downwards, rolling-hinge fault.