Turbidity currents of high velocity may occur during catastrophic conditions, but our records suggest that currents of little more than 1 knot (= 0.5 m/s) may be quite common in submarine canyons. Our three current-meter records of such currents were obtained (1) during an onshore storm at La Jolla, California, (2) during relatively high swells off the Rio Balsas Delta in western Mexico, and (3) in Abra Canyon off the Abra Delta in northwest Luzon during flood conditions. A pattern observed in all these occurences included a preceding, relatively large, upcanyon flow, a rapid buildup of the downcanyon turbidity current, a slow decay, and a following interval of no current. These currents may be particularly common where deltas have built across the continental shelf and large masses of sediment are being introduced into canyon heads. These relatively weak currents may transport large quantities of sediment down the canyon.