For transferring a preferably band-shaped weft material from a feed unit to an insertion element of a weaving machine, a free end of the weft material is clamped in a clamping device, the free end is transferred to the insertion element, and then the clamping device is opened to release the weft material, which is then inserted by the insertion element. The clamping device is conveyed by a drive essentially in the direction of motion of the insertion element between at least two different operating positions.