A process for manufacturing ribbed tubes, wherein a stainless steel tube is provided with ribs by helicoidally winding a copper strip around it. In joining the tube and rib, the unmelted copper strip is set on the tube surface edgewise into a melted area produced by a laser beam exclusively on the tube surface, thereby bonding the strip onto the tube by the solidification of the melted tube material. In this manner ribbed tubes can be provided, featuring an internal tube made of corrosion-resistant stainless steel and a helicoidal rib made of copper for increasing the heat exchange surface of the tube, which is distinguished by high thermal conductivity.