The present invention relates to a process for purifying a syngas of the CO/H.sub.2 or N.sub.2/H.sub.2 type, which consists in removing CO.sub.2 and possibly other gaseous impurities (water, etc.) before the gas undergoes a cryogenic process. These impurities are adsorbed by the gas stream to be purified passing over an NaLSX-type zeolite and then desorbed during a regeneration step which may be performed by raising the temperature (TSA) and/or reducing the pressure (PSA or VSA).