A process and plant are proposed for separating a feed mixture predominantly or exclusively containing carbon monoxide and hydrogen, in which the feed mixture is subjected to a cryogenic separation process in which a carbon monoxide-rich liquid and at least one residual gas mixture which is depleted in carbon monoxide and enriched in hydrogen, in comparison with the feed mixture, are formed. It is intended that the at least one residual gas mixture is subjected to a membrane separation process in which at least one hydrogen-rich permeate and at least one carbon monoxide-rich retentate are formed, wherein the or at least one of the carbon monoxide-rich retentates is recirculated to the cryogenic separation process.