A process for purifying a gas stream containing at least one impurity chosen from the group formed by propane, nitrogen protoxide and ethylene, in which process: (a) the gas stream to be purified is brought into contact with at least one adsorbent including at least one X zeolite containing barium cations; (b) at least one impurity is adsorbed on the adsorbent. Preferably, the adsorbent includes particles of X zeolite exchanged to at least 70%, preferably at least 89%, with barium cations, it being possible for the adsorbent to furthermore include a bed of activated alumina particles which is located upstream of the bed of barium-exchanged X zeolite.