The use of membranes in the equipment of air separation unit for cleaning the neon- helium mixture from nitrogen presumes to obtain a neon-helium concentrate in the installations with the limited production of liquid cryogenic products. The important indices in such a process are the degree of extraction of the target components (neon and helium) as well as the concentration of nitrogen impurity in the production stream. Alternative calculations of the neon-helium mixture enrichment process on the polymeric membrane in a wide range of operating modes have been presented. The dependence of the extraction degree of the neon-helium mixture on the initial concentration of nitrogen impurity at various recycle ratios has been demonstrated. It was found that recirculation of the permeate stream allowed to approximate the characteristics of the membrane installation to the characteristics of the dephlegmator.