Process for producing a polyalkenamer-containing composition, comprising the steps of: a) reacting at least one cycloalkene by ring-opening metathesis polymerization in at least one organic solvent to obtain a polyalkenamer-containing product mixture, wherein the polymerization is performed in the presence of at least one metal-containing catalyst and wherein the metal is selected from rhenium, ruthenium, osmium or mixtures thereof, wherein the cycloalkene is selected from the group consisting of cyclobutene, cyclopentene, cycloheptene, cyclooctene, cyclononene, cyclodecene, cyclododecene, cycloocta-1,5-diene, 1,5-dimethylcycloocta-1,5-diene, cyclodecadiene, norbornadiene, cyclododeca-1,5,9-triene, tri-methylcyclododeca-1,5,9-triene, norbornene (bicyclo[2.2.1]hept-2-ene), 5-(3'-cyclohexenyl)-2-norbornene, 5-ethyl-2-norbornene, 5-vinyl-2-norbornene, 5-ethylidene-2-norbornene, dicyclo-pentadiene and mixtures thereof, b) adding at least one alkyl vinyl derivative selected from C1- to C12-alkyl vinyl ethers, C1-C12-alkyl vinyl sulfides or mixtures thereof after the polymerization, wherein the amount of substance of the alkyl vinyl derivative corresponds at least to the amount of substance of catalyst, c) adding at least one compound A after addition of the alkyl vinyl derivative, wherein the amount of substance of the compound A corresponds at least to the amount of substance of catalyst, and wherein the compound A has at least one of the features i) or ii): i) at least one functional group selected from primary amino groups, secondary amino groups, tertiary amino groups, thiol groups, ester groups, carbonate ester groups, acetal groups, aldehyde groups, carbonyl groups, carboxamido groups, imido groups, oxime groups, thioester groups, nitrile groups, thiocyanate groups, primary ketimino groups, secondary ketimino groups, primary aldimino groups, secondary aldimino groups, sulfinyl groups, amino oxide groups, carboxyl groups, phosphino groups, phosphane oxide groups, phosphono groups or ii) at least one saturated or unsaturated aliphatic or aromatic heterocyclic ring having 3 to 14 ring atoms, wherein the ring atoms contain at least one carbon atom and at least one atom selected from oxygen, nitrogen and sulfur and d) working up the product mixture to remove the catalyst to obtain the polyalkenamer-containing composition, wherein the workup is carried out by membrane filtration in at least one organic solvent, wherein the polymer is dissolved during the membrane filtration. a) reacting at least one cycloalkene by ring-opening metathesis polymerization in at least one organic solvent to obtain a polyalkenamer-containing product mixture, wherein the polymerization is performed in the presence of at least one metal-containing catalyst and wherein the metal is selected from rhenium, ruthenium, osmium or mixtures thereof, wherein the cycloalkene is selected from the group consisting of cyclobutene, cyclopentene, cycloheptene, cyclooctene, cyclononene, cyclodecene, cyclododecene, cycloocta-1,5-diene, 1,5-dimethylcycloocta-1,5-diene, cyclodecadiene, norbornadiene, cyclododeca-1,5,9-triene, tri-methylcyclododeca-1,5,9-triene, norbornene (bicyclo[2.2.1]hept-2-ene), 5-(3'-cyclohexenyl)-2-norbornene, 5-ethyl-2-norbornene, 5-vinyl-2-norbornene, 5-ethylidene-2-norbornene, dicyclo-pentadiene and mixtures thereof, b) adding at least one alkyl vinyl derivative selected from C1- to C12-alkyl vinyl ethers, C1-C12-alkyl vinyl sulfides or mixtures thereof after the polymerization, wherein the amount of substance of the alkyl vinyl derivative corresponds at least to the amount of substance of catalyst, c) adding at least one compound A after addition of the alkyl vinyl derivative, wherein the amount of substance of the compound A corresponds at least to the amount of substance of catalyst, and wherein the compound A has at least one of the features i) or ii): i) at least one functional group selected from primary amino groups, secondary amino groups, tertiary amino groups, thiol groups, ester groups, carbonate ester groups, acetal groups, aldehyde groups, carbonyl groups, carboxamido groups, imido groups, oxime groups, thioester groups, nitrile groups, thiocyanate groups, primary ketimino groups, secondary ketimino groups, primary aldimino groups, secondary aldimino groups, sulfinyl groups, amino oxide groups, carboxyl groups, phosphino groups, phosphane oxide groups, phosphono groups or ii) at least one saturated or unsaturated aliphatic or aromatic heterocyclic ring having 3 to 14 ring atoms, wherein the ring atoms contain at least one carbon atom and at least one atom selected from oxygen, nitrogen and sulfur and i) at least one functional group selected from primary amino groups, secondary amino groups, tertiary amino groups, thiol groups, ester groups, carbonate ester groups, acetal groups, aldehyde groups, carbonyl groups, carboxamido groups, imido groups, oxime groups, thioester groups, nitrile groups, thiocyanate groups, primary ketimino groups, secondary ketimino groups, primary aldimino groups, secondary aldimino groups, sulfinyl groups, amino oxide groups, carboxyl groups, phosphino groups, phosphane oxide groups, phosphono groups or ii) at least one saturated or unsaturated aliphatic or aromatic heterocyclic ring having 3 to 14 ring atoms, wherein the ring atoms contain at least one carbon atom and at least one atom selected from oxygen, nitrogen and sulfur and d) working up the product mixture to remove the catalyst to obtain the polyalkenamer-containing composition, wherein the workup is carried out by membrane filtration in at least one organic solvent, wherein the polymer is dissolved during the membrane filtration.