Method for twisting a plurality of single lines (L1-L4), in which (a) the single lines (L1-L4) are introduced into clamps of a fixing unit at a first position, wherein the contact pressure of the clamps is for this purpose reduced so that, although the single lines (L1-L4) can be drawn through the clamps, said contact pressure is still high enough that the single lines (L1-L4) are held tautly on account of friction arising during the drawing-in operation, (b) the single lines (L1-L4) are fastened in respective mounting elements of an untwisting unit at a second position that is spaced apart from the first position in a longitudinal extent of the single lines (L1-L4), (c) the single lines (L1-L4) are introduced into a twisting unit so as to be longitudinally displaceable between the first position and the second position, (d) the single lines (L1-L4) are tensioned between the fixing unit and the untwisting unit as a result of movement of the fixing unit and/or of the untwisting unit, (e) the single lines (L1-L4) are twisted by means of a rotational movement of the twisting unit, wherein the twisting unit is moved in a direction of movement from the direction of the fixing unit in the direction of the untwisting unit, (f) the untwisting unit with the single lines (L1-L4) performs a rotational movement corresponding to and oriented in the same direction as the rotational movement of the twisting unit in such a manner that the mounting elements are rotated about a common axis of rotation by a common, collective rotational movement corresponding to the rotational movement of the twisting unit, and in addition the mounting elements themselves are rotated in the opposite direction to the collective rotational movement. (a) the single lines (L1-L4) are introduced into clamps of a fixing unit at a first position, wherein the contact pressure of the clamps is for this purpose reduced so that, although the single lines (L1-L4) can be drawn through the clamps, said contact pressure is still high enough that the single lines (L1-L4) are held tautly on account of friction arising during the drawing-in operation, (b) the single lines (L1-L4) are fastened in respective mounting elements of an untwisting unit at a second position that is spaced apart from the first position in a longitudinal extent of the single lines (L1-L4), (c) the single lines (L1-L4) are introduced into a twisting unit so as to be longitudinally displaceable between the first position and the second position, (d) the single lines (L1-L4) are tensioned between the fixing unit and the untwisting unit as a result of movement of the fixing unit and/or of the untwisting unit, (e) the single lines (L1-L4) are twisted by means of a rotational movement of the twisting unit, wherein the twisting unit is moved in a direction of movement from the direction of the fixing unit in the direction of the untwisting unit, (f) the untwisting unit with the single lines (L1-L4) performs a rotational movement corresponding to and oriented in the same direction as the rotational movement of the twisting unit in such a manner that the mounting elements are rotated about a common axis of rotation by a common, collective rotational movement corresponding to the rotational movement of the twisting unit, and in addition the mounting elements themselves are rotated in the opposite direction to the collective rotational movement.