The central Red Sea, an oceanic basin floored by Miocene evaporites reaching kilometers in thickness in places, is at an early stage of development, where seafloor spreading has geologically only recently replaced continental rifting. Surveys using a high-resolution multibeam echo sounder around Thetis Deep, a new spreading center, have revealed a remarkable series of structures resembling viscous gravity flows, which are here interpreted as originating from flowage of the evaporites laterally unloaded by axial rifting and other processes developing the relief of the deep. The flow margins are marked by stream-wise lineaments and some apparently rotated markers. Their fronts in the floor of the deep are rounded in plan view and profile. Their surfaces contain small, closely spaced features resembling extensional faults. In one area below declining gradients, the surface contains along-slope ridges and valleys typical of compression folds (ogives). Flow-parallel lineaments and extensional faults lie, respectively, parallel and orthogonal to the direction of maximum seabed gradient. Movement is apparently heterogeneous, at least in part because of varied blocking by relief in underlying basement observed protruding between flows. Flowage is currently transporting materials into the floor of the deep where they have the potential to become incorporated into the young oceanic crust by repeated eruption of axial lavas over them. In the light of these new data, we reexamine the possibility and implications of flowage in the South Atlantic marginal evaporites, in particular, whether flowage contaminated early oceanic crust in such areas.