It has long been known that pillow basalts are a dominant feature of oceanic volcanism on midocean ridges. Recent studies in the Cayman Trough, East Pacific Rise, and Galapagos Rift valley have shown that sheet flows are also an important component, especially on ridges with intermediate and fast opening rates. This paper describes the surface forms of such sheet flows observed in the Galapagos Rift valley. The principal types are lobate, smooth, rippled, and wrinkled, as well as hackly and jumbled forms. Collapse pits of a wide range of sizes are common; they appear to result from subsidence of the lava as a consequence of distal spreading of the flow and/or headward drainback into the subsurface plumbing system. Lava pillars are numerous around collapse pits, and current evidence suggests that they most likely are spiracles produced by water trapped below an advancing flow and rising through it to the surface. From Hawaiian analogs we conclude that sheet flows can be considered a submarine equivalent of surface-fed pahoehoe, while the pillow basalts are analogous to subaerial tubefed pahoehoe. We view the difference between sheet flows and pillow basalts to be the result of different degrees of channelization and rates of delivery of lava to flow fronts, associated with differences in duration and rate of eruption. In this model the sheet flows and pillowed ridges of the Galapagos Rift are the analogs of the early and the late products of an Hawaiian eruptive event, respectively. The sheet flows represent early, brief but voluminous eruptions. These are followed by more sustained, slower but steadier eruptive phases that produce pillow basalts after an internal plumbing system has been well established. Thus pillowed volcanics should normally overlie sheet flow complexes of only slightly greater age, and stratigraphie sections accumulated over long intervals should consist of alternating sequences of sheet and pillow flows. This model leads to several different ways of explaining the distinction between the apparent dominance of pillows on slow spreading ridges and the sheet flow and pillow complexes on faster spreading ridges.