Along a row of spindles of a ring-spinning machine, an underwind-residue remover is displaceable by a belt whose belt stretches are horizontal and lie one above the other over the length of the machine. The underwined-residue remover has a shank guided along a rib at a track for the remover alongside a row of spindles and the track has a foot extending horizontally from the rib and overlain by the stretches of the belt. The stretches of the belt have loops connecting them at opposite ends and a roller arrangement about which the respective loop passes.