The net sediment transport under regular waves and under wave groups with and without bound long waves is investigated by mathematical modeling. The bed is assumed to be plane (sheet flow conditions), which occurs for Shields parameters larger than about 1. The turbulent boundary layer flow is modeled by a mixing length model. The suspended sediment is modeled by the advection diffusion equation. The net sediment transport due to streaming, mass drift, and bound long waves is considered. It is found that the bound long waves cause an additional forward motion of the water near the bed. The bound long waves further give a negative contribution to the sediment transport because the backward motion in the long waves is coupled with the high waves and high sediment concentrations. The combined net sediment transport is found to depend on the grain size and the transport intensity: For very fine sand the mean water motion and the forward drift of the sediment dominate, giving a positive net transport. For coarser sand the coupling between backward motion and high sediment concentration dominates, giving a negative contribution. A parameter study is carried out to investigate the dependence of the net sediment transport on variations of the dimensionless parameters that characterize the condition. ¿ 1999 American Geophysical Union