Most of the world's rivers have discharged sediment on wide continental shelves and in estuaries since the last rise in sea level. In most cases, sediments are thus trapped on these areas and are not deposited on the now-relict submarine fans oceanward of these rivers. The conclusions are based on remote sensing, on data in the literature on present sedimentation rates on the shelves and the submarine fans, and on river sediment discharges for the 22 rivers studied. These submarine fans will remain cut off from their fluvial sources until the shelves and estuaries are filled and sediments can bypass these areas. The time required to fill these shelves and estuaries ranges from 2,600 to 3,400 yr for the Ganges-Brahmaputra to 1 to 1.2 m.y. for the Yenisei-Ob. For most river systems, sea level will change before shelves and estuaries are filled with sediments.