To vitrify chlorine-containing residues from flue gas cleaning, in particular filter dust and residues from the flue gas scrubber, the residues are melted in a melting furnace (8) and then discharged. To condition the melt, alkali-containing fluxes are added in the form of an oxide, hydroxide or carbonate, the stoichiometric ratio between the total alkalis and the chlorine being greater than 0.75, preferably greater than 1. Particularly suitable compounds in this process are oxides, hydroxides or carbonates of sodium or of potassium, or a mixture of such substances.