Physicochemical principles of membrane separation as applied to high purification of gases have been surveyed. The influence of impurity concentration in the feed gas and the membrane material on the separation factor and the role of sorption effects in the membrane material on the permeability and selectivity (separation factor) have been discussed. A mathematical model for the process of high gas purification in a radial membrane module has been developed. The efficiency of gas purification in the radial membrane module has been experimentally determined. The effect of longitudinal mixing in the membrane module on the purification efficiency has been theoretically and experimentally studied. The processes of high gas purification by membrane gas separation with recycle have been considered.