Seventeen sonobuoy refraction profiles have been shot to determine the nature of the basement and the broad pattern of sedimentation on the continental margin west of the outer Hebrides, NW Scotland. Under much of the shelf, crystalline rocks (Vp >5.1 km/s) lie within 100 m of the seafloor, the basemet being largely an extension of the Precambrian (Lewisian) metamorphic complex of western Scotland. Vp/Vs gives Poisson's ratios (&sgr;) of 0.26--0.30 for the Lewisian, values which are significantly higher than &sgr; in the deep crust under northern Britain, implying important compositional differences. Comparisons with ultrasonic velocities in rocks from the Scourian (~2700 Ma) and Laxfordian (~2200--1500 Ma) belts of the Scottish mainland suggest that the Lewisian on the inner continental shelf is predominantly Laxfordian (Vp ~5.5 km/s). Higher-velocity rocks, probably Scourian with only a moderate degree of Laxfordian reworking (Vp ~5.9 km/s), and Cenozoic intrusions occur locally. Two seismic profiles indicate that the outer continental shelf may be underlain by a zone of dense Scourian/early Laxfordian granulites, whose presence possibly influenced the siting of the continental slope. The sediments covering the basement are generally thin. Thickness exceeding 1 km are restricted to a faultbounded trough off the Isle of Lewis and to the outer shelf and continental slope. The deposits can be divided into Cenozoic (1.7--1.9 km/s) and Mesozoic (3.0--4.4 km/s) units, velocity variations in the latter probably reflecting the abundance of early Cenozoic basic intrusions. The distribution of the Mesozoic is partly controlled by faults which appear to be related to early Precambrian shear zones in the basement. These highly foliated belts seem to have facilitated stress relief by normal faulting during Permo-Triassic rifting activity. The general lack of subsidence of the Outer Hebridean block is attributed to the buoyancy of granitic material incorporated at an early stage of its history.