Air is purified by being passed in sequence through a first, lower, bed of activated alumina particles which adsorb water vapor preferentially therefrom, and a second, upper, bed of zeolite 13X molecular sieve particles which adsorb carbon dioxide preferentially therefrom. The air passes upwardly through the first bed and downwardly through the second bed. Once fully loaded with the adsorbent components, the beds and are regenerated by the passage therethrough of hot regeneration gas. one part of the regeneration gas flows downwardly through the first bed; another part flows upwardly through the second bed. The hot regeneration gas causes the previously adsorbed components to be desorbed. Once regeneration has ended, and the beds have returned their adsorbing temperature, they may be used again to purify air.