A pressurized gaseous mixture acidic gas and a useful gas is directly in a first absorption column with a physically acting absorption agent. Then the absorption agent loaded with the acid gas and useful gas is subdivided into first and second streams. The first stream is fed directly to a recycle flash container and there decompressed to reclaim the useful gas, extract the acidic gas from the absorption agent, and form a recycled gas containing the useful gas and acidic gas. The second stream is through a second absorption column to the recycle flash container. Some of the recycled gas from the recycle flash container is compressed and fed through the second absorption column so as to therein directly contact the second stream, and then the recycle gas that has passed through the second absorption column and contacted the second stream is returned to the gaseous mixture.