A description is given of compositions comprising a chlorine-containing polymer and at least one compound of the general formula I where x is oxygen or sulfur, and R is C2-C22-acyloxyalkyl or C1-C12-alkyl which may be interrupted by 1 to 3 oxygen atoms and/or substituted by 1 to 3 OH groups, or is C3-C8-alkenyl, C7-C10-phenylalkyl, C5-C8-cycloalkyl, C7-C10-alkylphenyl, phenyl or naphthyl, where the aromatic radical in each case may be substituted by —OH, C1-C12-alkyl and/or OC1-C4-alkyl, and R1 is hydrogen or is as defined for R.