An air prepurification process carried out in a battery of three adsorption vessels arranged in parallel. The process includes three steps: a first step in which non-steady state PSA is carried out in the first and second vessels operated in alternating adsorption and bed regeneration mode while the adsorbent in the third vessel undergoes thermal regeneration; a second step in which non-steady state PSA is carried out in the second and third vessels operated in alternating adsorption and bed regeneration modes while the adsorbent in the first vessel undergoes thermal regeneration; and a third step in which non-steady state PSA is carried out in the first and third vessels operated in alternating adsorption and bed regeneration modes while the adsorbent in the second vessel undergoes thermal regeneration. Each vessel contains at least two adsorbent layers, including a first layer of activated alumina, which adsorbs substantially all moisture and some carbon dioxide from the feed air, and a second layer of zeolite, which adsorbs substantially all of the remaining carbon dioxide in the feed air. The feed air may be passed through beds of hydrogen oxidation and carbon monoxide oxidation catalysts positioned between the first and second layers, to convert any hydrogen and carbon monoxide in the feed air to water vapor and carbon dioxide, respectively, these components being removed from the feed air as it passes through the layer of zeolite.