A process for the continuous preparation of a 1,3-dioxolan-2-one of the general formula I where R 1 is hydrogen or an organic radical having from 1 to 40 carbon atoms, R 2 and R 3 are each, independently of one another, hydrogen or C 1 -C 4 -alkyl, where R 2 and R 3 may also be joined to one another to form a five- or six-membered ring, wherein: a) an oxirane of the general formula II where R 1, R 2 and R 3 are as defined above, is reacted with carbon dioxide in the liquid phase in the presence of a catalyst dissolved homogeneously in the liquid phase in a reaction zone, b) a liquid discharge comprising polymeric by-products of the reaction is taken from the reaction zone and subjected to a work-up comprising fractionation by means of a semipermeable membrane to give a permeate and a retentate, with a high molecular weight fraction of the polymeric by-products being retained by the membrane, a stream consisting essentially of the compound, the catalyst and the polymeric by-products being separated off from the discharge from the reaction zone in step b) and being subjected at least partly to the fractionation by means of a semipermeable membrane, with the catalyst passing at least partly into the permeate, with the permeate comprising at least 70% of the catalyst comprised in the stream used for the membrane separation, and c) a purge stream comprising the high molecular weight fraction of the polymeric by-products is provided from the retentate. R 1 is hydrogen or an organic radical having from 1 to 40 carbon atoms, R 2 and R 3 are each, independently of one another, hydrogen or C 1 -C 4 -alkyl, where R 2 and R 3 may also be joined to one another to form a five- or six-membered ring, wherein: a) an oxirane of the general formula II where R 1, R 2 and R 3 are as defined above, is reacted with carbon dioxide in the liquid phase in the presence of a catalyst dissolved homogeneously in the liquid phase in a reaction zone, b) a liquid discharge comprising polymeric by-products of the reaction is taken from the reaction zone and subjected to a work-up comprising fractionation by means of a semipermeable membrane to give a permeate and a retentate, with a high molecular weight fraction of the polymeric by-products being retained by the membrane, a stream consisting essentially of the compound, the catalyst and the polymeric by-products being separated off from the discharge from the reaction zone in step b) and being subjected at least partly to the fractionation by means of a semipermeable membrane, with the catalyst passing at least partly into the permeate, with the permeate comprising at least 70% of the catalyst comprised in the stream used for the membrane separation, and c) a purge stream comprising the high molecular weight fraction of the polymeric by-products is provided from the retentate. a) an oxirane of the general formula II where R 1, R 2 and R 3 are as defined above, is reacted with carbon dioxide in the liquid phase in the presence of a catalyst dissolved homogeneously in the liquid phase in a reaction zone, b) a liquid discharge comprising polymeric by-products of the reaction is taken from the reaction zone and subjected to a work-up comprising fractionation by means of a semipermeable membrane to give a permeate and a retentate, with a high molecular weight fraction of the polymeric by-products being retained by the membrane, a stream consisting essentially of the compound, the catalyst and the polymeric by-products being separated off from the discharge from the reaction zone in step b) and being subjected at least partly to the fractionation by means of a semipermeable membrane, with the catalyst passing at least partly into the permeate, with the permeate comprising at least 70% of the catalyst comprised in the stream used for the membrane separation, and c) a purge stream comprising the high molecular weight fraction of the polymeric by-products is provided from the retentate.