A method and an apparatus for producing metallic semi-finished products by means of remelting and/or remelt-alloying. Here, the material is melted selectively locally in a melting capillary in the material volume by means of high-energy, focused radiation, the melting capillary is moved through the material and the material is cooled down at a high cooling rate by means of a cooled heat sink, which is located close to the melting capillary and coupled to the material in a well heat-conductive manner.
