Abstract: A plurality of elongated elements is maintained at a distance from one another by a spacing element, joined together at an inlet nipple, and twisted in the same twisting direction at a constant twisting speed by a twisting head located downstream of the inlet nipple, to emerge from the twisting head through an outlet nipple. The distance of the spacing element from the inlet nipple is cyclically varied by displacing the spacing element at a displacement speed which is lower than the advancement speed of the elements. The displacement speed is increased to the advancement speed during the displacement of the spacing element from a terminal position of a trajectory of displacement of the separating element which is more remote from the twisting head than the other terminal position, in a section of the trajectory having a length which is a predetermined fraction of the length of the trajectory.