Polymer-based polyvalent malonic acid derivatives having anti-adhesive properties are described. The compounds comprise a polyamino acid linked to a group of formula (I). In formula (I), R.sup.1 and R.sup.2 together form a six-membered carbocylic or heterocyclic ring, containing at least one substituent selected from R.sup.4, R.sup.5, and R.sup.6. R.sup.3 is H, (CH.sub.2) .sub.m X or CH.sub.2 O(CH.sub.2).sup.m X.sup.1. The polyamino acid and the group of formula II are linked via R.sup.4, R.sup.5, or R.sup.6, or optionally via a spacer of formula --�Q.sup.1 --(CH.sub.2).sub.p --Q.sup.2 --!.sub.r. A and B independently are O, S, NH, HN--CO, OC--NH, O--CO, OC--O, NH--CO--O, --O--CO--NH, S--CO, SC--O, O--CS--S, S--CS--OS, NH--CS--S, S--CS--NH, or CH.sub.2. Z is a pyranose, furanose, open-chain polyalcohol or Y--X.sup.6. Y is --O--(CX.sup.2,X.sup.3).sub.n, -(CX.sup.2,X.sup.3).sub.n, --CH.sub.2 --(CX.sup.2,X.sup.3).sub.n or a saturated or unsaturated six-membered carbo- or heterocyclic group having at least one substituent R.sup.9, or a combination of the chain --O--(CX.sup.2,X.sup.3).sub.n, or -(CX.sup.2,X.sup.3).sub.n, and the carbocyclic or heterocyclic group, in which R.sup.4, R.sup.5, and R.sup.6 independently are H, OH, --O--(CH.sub.2) .sub.q X.sup.4, --CH.sub.2 O(CH.sub.2) .sub.q X.sup.5, or HNC(O)CH.sub.3, and X, X.sup.1, X.sup.2, and X.sup.3 independently are H, NH.sub.2, COOH, OH, CH.sub.2 OH, CH.sub.2 NH.sub.2, C.sub.1 -C.sub.20 -alkyl, or C.sub.6 -C.sub.10 -aryl, X.sup.4 and X.sup.5 independently are --NH-- or --O--, and X.sup.6 is OH or --C(R.sup.3) (COOH).sub.2. m, n, and q independently can be 1-20. In the linker, Q.sup.1 is CH.sub.2 or --CO--, Q.sup.2 is --NH-- or --CO--NH--, p is 1-6, and r is 0 or 1. Methods of preparing the compounds, and their use as medicaments or diagnostic agents also are disclosed. ##STR1##