The invention relates to a method and device for the continuous production of steel using metal charge material (8) that is preheated in an upper part of a melting vessel (2), is then melted in a lower part (9) of the melting vessel l(2) with fossil fuels (23) and the molten material (16) is continuously discharged into a treatment vessel (3) in which the desired steel quality is adjusted while gases (22) are introduced into the melting vessel (2) from the exterior to afterburn the melting exhaust gases (13). The aim of the invention is to improve the aforementioned afterburn step while at the same time reducing oxidation of the iron-containing charge materials. For this purpose, the process gases (13) are step-wise afterburned when ascending in the melting vessel (2) by introducing the afterburn gases (22) into the interior of the charge material column by way of an interior shaft (5) that projects into the material column and in whose walls (20) inlet openings (21) for the gases (22) are disposed and form afterburn planes (E1, E2) arranged one on top of the other. The invention also relates to a device for carrying out the inventive method.