A polymerisation-curable composition for the production of biodegradable, biocompatible, crosslinked polymers, contains 5-100 wt.% special vinyl carboxylate monomer(s), vinylcarbonate monomer(s) (or corresponding monomers with sulfur, nitrogen or phosphorus instead of one of the oxygen atoms in the carbonate group) and/or vinyloxyphosphonic acid monomer(s). A polymerisation-curable composition (PCC) for the production of biodegradable, biocompatible, crosslinked polymers (preferably based on polyvinyl alcohol), comprising (a) 5-100 wt.% vinyl ester monomer(s) of formula (I), (II) and/or (III). X : O, S, N or P; n : 1-1000, preferably 1-3, with at least 20% of the n= at least 2; R 1>;(i) H, n-valent 1-30C (preferably 5-15C) hydrocarbon groups (optionally with in-chain and/or terminal O, S, N and/or P atoms and optionally substituted with OH, COOH, CN, CHO or=O), or (ii) n-valent residues of biodegradable, biocompatible oligomers or polymers selected from polysaccharides, polypeptides, polyamides, polyesters, polycarbonates, polyethers and fatty acid derivatives; m : 0-4; R 2>;H, OH,=O or other options as for R 1>;; R 3>;H, OH or other options as for R 1>; , (b) 0-50 wt.% unsaturated comonomers selected from (meth)acrylic acid, maleic acid, fumaric acid. vinylpyrrolidone and alpha -olefin comonomers, (c) 0-10 wt.% thermal and/or photo-initiator(s) and (d) 0-95 wt.% solvent(s) selected from water, lower alcohols, ethers, ketones, esters, amides and hydrocarbons.Independent claims are also included for (1) biodegradable, biocompatible, crosslinked polymers (BBCP) based on this PCC (2) a method for the production of BBCP by polymerisation of PCC (3) new compounds of formula (I), (II) and (III) (see below) . [Image].