A process is disclosed for the purification of a gaseous mixture, for example, consisting essentially of hydrogen and containing impurities, e.g., carbon monoxide, methane and argon. The gaseous mixture is scrubbed with liquid nitrogen in a scrubbing column having two sections. In order to be able to process the residual gases formed during the scrubbing step, containing especially CO, argon and CH.sub.4, in a simple way and without great investment costs, liquid nitrogen is introduced in a quantity sufficient for an almost complete scrubbing out of the carbon monoxide, and a partial amount of the scrubbing liquid, enriched with carbon monoxide, is withdrawn between the upper and lower sections. The partial amount withdrawn is dimensioned so that the residual quantity of scrubbing agent delivered to the lower section of the scrubbing column is enough to scrub out the methane from the gaseous mixture, but yet also leaves a major portion of the carbon monoxide in the gaseous mixture.