While the transport of sediment by unidirectional currents or by oscillatory (wave-induced) currents has been investigated, very little attention has been paid to the problem of the threshold of transport under the two mechanisms combined. Studies were carried out using cohesionless sand-sized (mean diameters: 142, 363, 771 and 1134 μm) quartz grains in a unidirectional flume, within which an oscillatory carriage had been installed. The experiments were carried out under unidirectional velocities ranging between 0 and 27 cm s-1, combined with simulated wave-induced currents (at periods of 5 and 15 s) ranging from 0 to 35 cm s-1. The threshold of transport was assessed, by visual observation, using the Yalin Criterion for unidirectional flow. This criterion permitted critical conditions to be estimated subjectively by observation of incipient transport from the flat beds. The results indicated the dependence of the critical threshold velocity combination on grain size and wave period. Thresholds tend to increase with increasing grain size or decreasing period. The grain-size dependence is predictable from existing empirical relationships for the separate mechanisms; statistical fluctuations in near-bed stress (bursting) however, are invoked to explain the wave period dependence. The latter effect acts in a reverse manner for wave and current combinations than for waves alone. Graphs are presented, relating grain size to critical threshold velocity combinations, to aid in the sedimentological interpretation of field data.