Modern steel production processes require precise knowledge of the current composition and temperature of the liquid metal being processed. In particular during steel production in a converter, high match rates for final carbon content and bath temperature are required. Quantitatively precise blowing of oxygen corresponding to the final target carbon content, and the metal temperature, are decisive factors affecting the economic efficiency of the process and the quality of the steel produced. In order to allow relatively precise process monitoring, various processes and procedures are known, the application thereof being based on measuring exhaust gas composition and on mass flow balances. All models work at an exactness that depends on the precision of the input data, particularly with respect to the weight data of the raw materials and the chemical properties of the metal used. In order to allow control of the converter process for producing steel independently of the predefined process model, in particular when blowing oxygen, the invention proposes that detected values for the critical decoking point (t′crit) and for the end of O2-blowing (t′EoB) are obtained by means of a submodel operating as a process monitor based on the exhaust gas analysis and independent of the process model, by sensibly combining the constituent signals obtained, by means of which values the oxygen content predicted by the process model is corrected at the start of the process and matched to the actual conditions near the end of the decoking period.