Abstract: A process of continuous production of seam-welded steel tubing is concerned.A steel strip is taken out from a strip coil and conveyed to a tube-preshaping step including a plural of shaping roll stand positions. In the preshaping step, the strip is laterally rounded up gradually from band strip to a rough-shaped tubing until the side edges are brought into a mutually abutting state ready for seam-welding. The preshaping step is divided into a plurality of local regions. In these local regions, substantially body portion with exception of corresponding marginal edge zones of the tubing stock is separately subjected to heating. The heating width and heating intensity at these regions are increased stepwise as the tubular stock advances from upstream to downstream for avoiding conventionally appearing edge wavings and buckling undulations in the material of the steel tubing.