A method and apparatus for drying a natural gas or an industrial gas that contains acidic gas components, wherein gas drying is followed by the removal of the acidic gas components from the dried gas. The same physical solvent is used for both of the process steps of gas drying and of acidic gas removal. The gas to be dried is brought into contact with the physical solvent, which absorbs most of the water contained in the gas. The physical solvent, loaded with water, is transferred into a solvent regenerating device to be heated where the water contained in the solvent is stripped from the solvent in the countercurrent by acidic gas that is removed from the dried useful gas during the acidic gas absorption. The acidic gas being released again in the acidic gas solvent regenerating device, stripped from the solvent, and discharged from the solvent regenerating device.