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On river-influenced continental margins, terrigenous muds tend to accumulate in the middle of the continental shelf. The common occurrence of mid-shelf mud belts has been attributed to three basic across-margin transport mechanisms. Muds either diffuse to the mid-shelf under the influence of storms, or they are advected there by oceanographic currents, or they arrive at the mid-shelf in dense suspensions that flow across the margin under the influence of gravity. Until recently, observations generally favoured the hypothesis that ocean currents are responsible for advecting dilute suspensions of mud to the mid-shelf. Transport by dense gravity flows was widely rejected, based primarily on the arguments that the bathymetric gradients of continental shelves are too small to sustain gravity flows, and that sediment concentrations cannot grow large enough to cause suspensions to flow down gradient. Observations conducted on the Eel River continental shelf off northern California, however, demonstrate that cross-margin transport by dense suspensions can be an important mechanism for the emplacement of muds on the mid-shelf. Dense suspensions form near the seabed when sediment in the wave boundary layer cannot deposit because of stress exerted on the bottom by waves, and when sediment does not diffuse out of the wave boundary layer because of relatively weak current-induced turbulence. In the future, the importance of these flows on other margins needs to be assessed.