To produce threaded steel tension members, steel is used with a C-content of 0.50 to 0.80%, preferably 0.75%, a Si-content of 0.20 to 0.50%, preferably 0.25%, and a Mn content of 0.30 to 0.80%, preferably 0.60%. Exiting from the rolling heat at the outlet side of the finishing stand after hot rolling, the tension member or rod is subjected to surface quenching by a cooling medium, preferably water, so that the steel in a rim zone R.sub.1 is transformed immediately and completely into martensite, while the heat content remaining in the core zone K.sub.1 does not effect a tempering of the martensite rim zone during the subsequent cooling beyond the range of the intermediate stage. Steel tension members of this type have a high ductility and toughness at a high yield limit and high strength, they are corrosion-resistant to a great degree and have a wear resistant surface which makes them particularly suitable for threaded tension rods in which the threads are produced either by a cold forming operation or hot rolled ribs.