Intense transport of sediment is studied in flows of steep slopes. Transport- and friction formulae suitable for flows at high shear stress above eroded bed are discussed. The formulae are further incorporated to a proposed simple model for open-channel flow with gradually varied transport of sediment. Two variants of the formulae are used alternatively in the model. Tilting-flume experiments are described that provided steady-flow data suitable for a validation of the formulae and unsteady-sediment-transport data for a validation of the designed model of gradually varied transport. A comparison of experimental results with formulae predictions and model simulations shows a very reasonable agreement for both variants of the transport and friction formulae. and Obsahuje seznam literatury a znaků