To maintain a riser under tension, the riser can be connected to a gripper means (5, 12) which is connected to vertical toothed racks (4) that are in constant engagement with gear wheels (22) which are driven with constant torque, preferably by hydraulic motors (9) at constant pressure. An apparatus is also described for putting the riser under tension. The apparatus includes vertical guides (7) in a derrick, toothed racks (4) in the vertical guides (7), a gripper means (5, 12) designed for interaction with a riser connected to the racks (4), and drive units (9) arranged in the derrick for drive-actuation of the racks (4) in the vertical guides (7).