The invention relates to a process and a device for the cryogenic separation of a methane-containing feed gas (1) that predominantly consists of hydrogen and carbon monoxide, which feed gas is partially condensed in this case by cooling, in order to obtain a hydrogen-containing first liquid phase (9) that predominantly consists of carbon monoxide and methane, from which first liquid a second liquid phase (15) is generated in an H2 stripping column (T1) by separating off hydrogen, from which second liquid phase (15), in a CO/CH4 separation column (T2), a carbon monoxide-rich gas phase (31) is obtained at a purity which permits its release as carbon monoxide product (32) and also a sump product (34) predominantly consisting of methane and carbon monoxide is obtained, wherein heat is withdrawn from a refrigerant (20) that is conducted through a cooling circuit driven by a circuit compressor (V), and used for heating the CO/CH4 separation column (T2). It is characteristic in this case that heat is withdrawn from at least a part (2) of the feed gas (1) and used for heating the CO/CH4 separation column (T2).