In a process for the continuous production of helical or annular corrugated, thin-walled, in particular longitudinally welded metal tubes, in which a freely rotating roller ring in a turntable corrugation head, which is eccentric with respect to the smooth metal tube, rolls against the smooth surface of the metal tube to produce the corrugation, and the metal tube is transported by a traction device that grips the smooth and/or corrugated metal tube, the force acting on the roller ring is constantly measured, and the rotation speed of the head is controlled as a function of the measured force.