Abstract: The invention relates to a process for separating mixtures of hydrocarbons, notably conjugated diene hydrocarbons or aromatic hydrocarbons, from mixtures containing the same, by the general technique of permeation or pervaporation through specific membranes.The specific membranes used are formed of a high polymer comprising functional groups chemically combined by covalent bonding within the polymer forming the said membrane, the said groups possessing a physicochemical affinity, notably a capacity to complex, with respect to one of said hydrocarbons and, substantially, the absence of such a capacity with respect to other hydrocarbons of the mixture. For the separation of dienes, such as butadiene and pentadiene, membranes are used containing active nitrile, pyrrolidone, N-substituted groups, such as N-alkyl groups, preferably N-vinyl or N-methyl-pyrrolidone. The membrane can be obtained, for example, by copolymerization of butadiene with acrylonitrile, with the membrane containing about 2.