NOVELTY - Desulfurizing a gas mixture containing hydrogen sulfide and carbon dioxide by selective absorption of the hydrogen sulfide, comprises: (i) utilizing a combustible biogas containing hydrogen and/or methane as the gas mixture to be desulfurized; (ii) performing a phase separation step after the absorption step for separating the liquid phase in the form of the sulfide-enriched absorbent from the gas phase containing the combustible gas components; and (iii) contacting the degassed liquid phase with an oxidizing agent for oxidizing the sulfide.    USE - The method is useful desulfurizing a gas mixture containing hydrogen sulfide and carbon dioxide (claimed).    ADVANTAGE - The method: allows liquid phase to simply pass to the oxidation reactor; and ensures good mixing at high flow rates in cost-efficient manner.    DETAILED DESCRIPTION - Desulfurizing a gas mixture containing hydrogen sulfide and carbon dioxide by selective absorption of the hydrogen sulfide into a basic absorbent and subsequent oxidation of the hydrogen sulfide absorbed with an oxidizing agent, comprises: (i) utilizing a combustible biogas containing hydrogen and/or methane as the gas mixture to be desulfurized; (ii) performing a phase separation step after the absorption step for separating the liquid phase in the form of the sulfide-enriched absorbent from the gas phase containing the combustible gas components; and (iii) contacting the degassed liquid phase with an oxidizing agent for oxidizing the sulfide to elemental sulfur and/or higher oxidation states of sulfur. An INDEPENDENT CLAIM is also included for a device for desulfurizing gas mixture containing hydrogen sulfide and carbon dioxide comprising at least one separator (3) arranged between at least one absorption reactor (1) and at least one oxidation reactor (2) for phase separating mixture of liquid phase and gas phase formed in at least one absorption reactor, and a gas-tight conduit (4) which opens out from at least one separator to the oxidation reactor for transferring the liquid phase.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic process flow for desulfurizing a gas mixture.    Absorption reactor (1)    Oxidation reactor (2)    Separator (3)    Gas-tight conduit (4)    Float-controlled surge arrester (5)