The invention relates to a drive device for multiaxial transport of workpieces through successive machining stations of a machine tool, in particular of a multistage forming press, wherein the drive device comprises two gripper rails, wherein the two gripper rails are transversely displaceable independently of each other by a first transverse drive assigned to the first gripper rail and a second transverse drive assigned to the second gripper rail for the execution of a closing movement. The gripper rails are here vertically displaceable independently of each other for the execution of a lifting movement, and/or the gripper rails are longitudinally displaceable independently of each other for the execution of a transport movement.