Abstract: For the purification of hydrocarbon-containing, e.g., methane raw gases containing H.sub.2 S and CO.sub.2, the raw gas is dried, and separated by rectification into a hydrocarbon-rich overhead fraction containing some H.sub.2 S and CO.sub.2 and into a bottom fraction consisting essentially of H.sub.2 S and CO.sub.2. The overhead product is freed, in a first scrubbing column, of the acidic components with a physical acting scrubbing medium selective for H.sub.2 S and COS as against CO.sub.2, e.g., polyethylene glycol ether or toluene. The bottom product from the rectification step is vaporized and selectively desulfurized in a second scrubbing column with the same scrubbing medium, and the scrubbed gas from the second scrubbing column is discharged as CO.sub.2 under pressure.