A gripper for electrical or optical lines (24, 24′) such as wires, cables, line bundles, optical fibers has two gripper jaws (22, 22′) movable relative to a counterbearing as well as relative to one another. Twisting heads (4) for twisting apparatuses for the lines (24, 24′) are equipped with such grippers. The gripper and the twisting head (4) and the twisting apparatus are provided with a drive arrangement including at least one adjustable-force drive (17) that acts via a link chain (15, 19, 19′, 20, 20′) on gripper jaw (22, 22′). The link chain (15, 19, 19′, 20, 20′) in this case has a section (19, 19′) movable parallel to the drive (17), but in the opposite direction of movement.