The invention relates to membrane gas separation, in particular to a method of fractionating mixtures of low molecular weight hydrocarbons based on the capillary condensation of the mixture components in the pores of microporous membranes having uniform porosity and a pore diameter of 5 to 250 nm, wherein, for capillary condensation, the temperature of the membrane and the pressure on the permeate side are kept below the temperature and the pressure of the feed mixture. The method provides significantly increasing membrane permeability with respect to condensable components, and also component separation factors, while also allowing to avoid deep cooling of the gas stream fed to a membrane module, and to carry out gas separation under insignificant cooling of the membrane on the permeate side (down to -50° C.). The invention provides for energy-efficient fractionation of hydrocarbon mixtures, including separation and drying of natural and associated petroleum gases.