On a machine for bending rod-shaped or tubular workpieces, which includes a bending head having a bending mandrel mounted on a rotational axis and rotatable by means of a rotary drive, and having a clamping device for pressing the workpiece to be bent against a forming groove on the bending mandrel and also a feeding device for the workpiece to be processed, whereby the clamping device is positionable relative to the bending mandrel and can is also pivotable concentrically to the rotational axis of the bending mandrel, the clamping device is attached to two mutually independent rotary drives, one of which performs its pivoting movement about the rotational axis of the bending mandrel, and via the other of which it can be moved with respect to the bending mandrel by using an interposed conversion transmission that converts a rotary motion to a linear motion, whereby the bending head includes three concentrically nested rotary shafts for transmitting the drive of the three rotary drives to the bending mandrel, to the conversion transmission and to the clamping device, each of which is connected to one of the rotary drives.