A method for the continuous production of steel using metal charge material that is preheated in an upper part of a melting vessel, is then melted in a lower part of the melting vessel with fossil fuels and the molten material is continuously discharged into a treatment vessel in which the desired steel quality is adjusted while gases are introduced into the melting vessel from the exterior to afterburn the melting exhaust gases. The process gases are step-wise afterburned when ascending in the melting vessel by introducing the afterburn gases into the interior of the charge material column by way of an interior shaft that projects into the material column and in whose walls inlet openings for the gases are disposed and form afterburn planes arranged one on top of the other.