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We have studied the current-induced displacement of a domain wall (DW) in the permalloy (Py) layer of a Co/Cu/Py spin valve structure at zero and very small applied field. The displacement is in opposite direction for opposite dc currents, and the current density required to move DW is only of the order of For a back and forth DW motion between two stable positions is observed. We also discuss the effect of an applied field on the DW motion.