A depth-averaged two-dimensional model has been established to simulate unsteady flow and sediment transport in streams. The difference in flow and sediment velocities is considered. It has been found that the depth-averaged suspended-sediment velocity and the bed-load velocity are smaller than the depth-averaged flow velocity, inducing a time lag between water and sediment transport. The significance of this time lag increases as the sediment size increases. The exchange between the moving sediment and the bed material, which may induce a spatial lag, is modeled by a non-equilibrium transport approach. Tests using laboratory and field measurements have shown that the established model is capable of capturing the hysteresis between flow and sediment transport under unsteady conditions. It is demonstrated that the hysteresis is larger when the hydrograph has steeper rising and falling limbs, and the time delay increases downstream. A depth-averaged two-dimensional model has been established to simulate unsteady flow and sediment transport in streams. The difference in flow and sediment velocities is considered. It has been found that the depth-averaged suspended-sediment velocity and the bed-load velocity are smaller than the depth-averaged flow velocity, inducing a time lag between water and sediment transport. The significance of this time lag increases as the sediment size increases. The exchange between the moving sediment and the bed material, which may induce a spatial lag Tests using laboratory and field measurements have shown that the established model is capable of capturing the hysteresis between flow and sediment transport under unsteady conditions. It is demonstrated that the hysteresis is larger when the hydrograph has steeper rising and falling limbs, and the time delay increases downstream.