The invention relates to a composite membrane with a separation-active membrane layer and a supporting membrane, a process for the production of the same, and a process for using the same. The composite membrane according to the invention is distinguished by the fact that the separation-active membrane layer comprises a polymer hardened by electromagnetic radiation with a wavelength that is less than 800 nm and/or by electron beams. The process according to the invention is distinguished by the fact that a layer of a solution of a polymer that can be hardened by electromagnetic radiation with a wavelength that is less than 800 nm and/or by electron beams and an initiator substance is applied to a supporting membrane and subsequently is hardened by electromagnetic radiation and/or by electron beams. The use according to the invention serves to retain low-molecular substances from organic solutions.