When waste glass that is highly contaminated with organic impurities is melted, these impurities cause the appearance of so-called 'black grains ' which cannot be eliminated in a subsequent refining process and which therefore impair the quality of the glass. According to the invention, gas nozzles (19) for introducing oxygen are arranged in the area of the feed opening (4) of a melting aggregate (2) which is thermally connected to a combustion chamber (3). The organic constituents are thus oxidised specifically and removed as waste gas (21). The invention enables even very highly contaminated waste glass, such as glass fibres, to be fed back into the production process.