New experiments under sheet flow conditions were conducted in an oscillating water tunnel to study the effects of flow acceleration on sand transport. The simulated hydrodynamic conditions considered flow patterns that drive cross-shore sediment transport in the nearshore zone: the wave nonlinearities associated with velocity and acceleration skewness and a negative mean current, the undertow. Net transport rates were evaluated from the sediment balance equation and show that (1) the acceleration skewness in an oscillatory flow produces a net sediment transport in the direction of the highest acceleration; (2) the net transport in the presence of an opposing current is negative, against the direction of the highest acceleration, and reduces with an increase in flow acceleration; and (3) velocity skewness increases the values of the net onshore transport rates.