A process for producing a high-grade steel tube includes the steps of: providing a tubular blank of an austenitic high-grade steel, wherein the high-grade steel comprises in weight % no more than 0.02% carbon, no more than 1.0% manganese, no more than 0.03% phosphor, no more than 0.015% sulfur, no more than 0.8% silicon, no more than 17.5% t to 18.5% nickel, no more than 19.5% to 20.5% chromium, no more than 6.0% to 6.5% molybdenum, no more than 0.18% to 0.25% nitrogen, no more than 0.5% to 1.0% copper, and a remainder of iron and unavoidable impurities; and cold-forming the blank into a tube.