A mixture of gases containing hydrogen and at least one further component, for example nitrogen and argon, is enriched in hydrogen in a separation stage by adsorption, or cooling and partial condensation and/or rectification and/or scrubbing. Upstream of this separation stage, at least part of the hydrogen is separated by membrane diffusion, thereby resulting in a highly improved process as compared to using either the separation stage or membrane diffusion alone, especially in connection with gaseous mixtures having components which are to be used at high pressures, e.g., a purge gas from an ammonia synthesis gas process.