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The continental margins of the southern and central Red Sea and most of Wilkes Land, Antarctica have bulk crustal configurations and detailed structures that are best explained by a prolonged history of magmatic expansion that followed a brief, but intense period of mechanical extension. Extension on the Red Sea margins was spatially confined to a rift that was 20–30 km in width. The rifting phase along the Arabian margin of the central and southern Red Sea occurred 25–32 Ma ago, primarily by detachment faulting at upper crustal levels and ductile uniform stretching at depth. Rifting was followed by an early magmatic phase during which the margin was invaded by dikes and plutons, primarily of gabbro and diorite, at 20–24 Ma, after the crust was mechanically thinned from 40 km to ≈ 20 km. We infer continued spreading after that in which broad shelves were formed by a process of magmatic expansion, because the offshore crust is only 8–15 km thick, including sediment, and seismic reflection data do not depict horst and graben or half graben structures from which mechanical extension might be inferred. The Wilkes Land margin is similar to the Arabian example. The margin is about 150 km in width, the amount of upper crustal extension is too low to explain the change in sub-sediment crustal thickness from ≈ 35 km on the mainland to < 10 km beneath the margin and reflectors in the deepest seismic sequence are nearly flat lying. Our model requires large volumes of melt in the early stages of continental rifting. The voluminous melt might be partly a product of nearby hot spots, such as Afar and partly the result of an initial period of partial fusion in the deep continental lithosphere under lower temperatures than ordinarily required by dry solidus conditions.