Abstract: Previous investigations of non-equilibrium and equilibrium sediment transport are analyzed and a two-dimensional mathematical model of non-equilibrium sediment transport in river channels with non-uniform bed material is presented.The concept of exchange rate of bed material is introduced,and a very short time step is used in the calculation.The main reason why the sediment recovering equilibrium distance for the non-uniform bed material is far longer than that for uniform bed material is discussed.Because the size composition of surface bed material is coarsened,the scouring of finer sand is farless than that for the initial state an d the distance of non-equilibrium sediment transport becomes much longer.A slower exchange rate of bed material then leads to a longer distance of non-equili brium sediment transport.