A method is disclosed for separating a multicomponent gas mixture comprising at least three components into three product streams by use of adsorbent membrane zones operating in series. Each product is enriched in a different component based upon the relative strength of adsorption of each component on the adsorbent material. A non-permeate primary component product is obtained by the selective adsorption and permeation through the adsorbent membranes of secondary components which are more strongly adsorbed than the primary components in the gas mixture. Two or more permeate streams enriched in the more strongly adsorbed components are withdrawn from the membrane zones as individual secondary products, each of which contains a different component distribution determined by the relative strength of adsorption of the secondary components on the adsorbent material. Increased recovery and product purity are realized by the integration of pressure swing adsorption (PSA) and cryogenic separation systems with the adsorbent membrane zones. PSA reject gas is used as a membrane sweep gas to increase the permeation rates of secondary components.