Apparatus for stranding elongated elements into a bundle of reversely twisted strand sections includes a rotating accumulator drum, a rotating winding flyer at the first end of the drum, and a rotating unwinding flyer at the second end of the drum. A guide plate and collector die guide the elements into the winding flyer, and a twist blocking device guides the twisted strands out of the unwinding flyer. A first twist of the bundle is produced by the winding flyer in a zone between collector die the winding flyer. A second reverse twist is produced by the unwinding flyer in the zone between the unwinding flyer and the twist blocking device. The winding flyer, the drum and the unwinding flyer rotate around a common axis, in the same direction, but at different speeds which change in alternating winding phases. The speed of the flyers and the drum are different from each other, but constant within the particular winding phase. The speeds of the flyers and drums are selected so that the strands are drawn through the apparatus at a predetermined speed and so that twisting in reverse direction occurs in alternating sections as the strands are drawn through the apparatus. The speed of rotation of the flyers and drums also determines the tightness of the twist. Durations of the periodically changing speeds are preferably selected such that the length of the bundle stranded in one direction is equal to the length stranded in the opposite direction.