The release of clear water from dams built across rivers running in alluvial sediments will cause bed degradation in the downstream channel. If this degradation went on unchecked, it would be a threat to the existing structures on the river, and might cause serious drainage problems in the cultivated areas on both sides of the river. A theory is presented to predict the ultimate conditions of bed armoring without sensible change in slope. The changes in bed roughness and in the regime of flow are both taken into consideration. The ultimate conditions of stable bed are obtained. The theory is then applied to the actual conditions of bed degradation of the Nile River after the closure of the Aswan High Dam in 1964. It is found that the general degradation in this particular case is not excessive, and does not need large scale protective measures or step-down weirs, to meet the probable change in the slope of river bed. However, the existing barrages on the Nile may need protection against any probable local or general scour.