Abstract: This invention pertains to an improved process for the removal of moisture from a moisture laden gas stream such as air utilizing a membrane dryer unit. The membrane dryer unit is equipped such that it incorporates a selective surface flow adsorbent membrane consisting essentially of an inorganic membrane material selected from the group consisting of alumina and silica gel membranes wherein the membrane has a thickness of approximately 0.5 to 50 microns with a mean pore size of less than about 15 A and preferably within about 4 to 10 A. In the cryogenic separation of air, an air stream contaminated with moisture and carbon dioxide is passed through the membrane dryer unit in countercurrent flow to a dry purge gas, wherein the water is selectively removed from the air stream. The partially dried air stream then is conveyed to an adsorption system operated under thermal swing or pressure swing conditions wherein the residual water and carbon dioxide are removed.