An improved two stage pressure swing adsorption process for producing enriched oxygen and separating nitrogen or oxygen from a feed air stream. The process utilizes two-stage pressure swing adsorption plants which are serially connected. In the first stage, carbon dioxide, water and part of nitrogen are removed and nitrogen is concentrated. In the second stage nitrogen is further separated from the effluent intermediate gas from the adsorption step in the adsorption towers of the first stage and oxygen is concentrated to the desired concentration. In the first stage the adsorption towers go through the steps in turn in a cycle: Adsorption, Purge, evacuation, countercurrent pressure equalization rising of the second stage gas, purge gas pressurization, and final pressurization. In the second stage the adsorption towers go through the steps in turn in a cycle: Adsorption, countercurrent pressure equalization falling, and final pressurization.