The present invention relates to a polymerization-curable composition for the preparation of biodegradable, biocompatible, cross-linked polymers on the basis of polyvinyl alcohol comprising: 5 to 100% by weight of (a) vinyl ester monomer(s) of one of the general formulas (I) to (III): wherein X is oxygen, sulfur, nitrogen, or phosphorus; n is 1 to 1000, at least 20% of the n being ≧2; the R1 are selected from hydrogen; straight, branched or cyclic, saturated or unsaturated, n-valent hydrocarbon groups having 1 to 30 carbon atoms, which optionally have heteroatoms and are optionally substituted with one or more substituents selected from —OH, —COON, —CN, —CHO, and ═O, and n-valent radicals of biodegradable, biocompatible oligomers and polymers; m is an integer from 1 to 5; the R2 are selected from hydrogen, —OH, ═O, and the options listed for R1; and the R3 are selected from hydrogen, —OH, and the options listed for R1; 0 to 50% by weight of ethylenically unsaturated co-monomers; 0 to 10% by weight of (a) polymerization initiator(s); and 0 to 95% by weight of solvent(s).