In polymer ammonium salts which are formed from a copolymer (A) which can be modified by a polymer-analogous reaction and from one or more amines (B), the copolymer (A) is obtainable by copolymerization of a monomer mixture of(a.sub.1) ethylene,(a.sub.2) acrylic acid and/or methacrylic acid, and(a.sub.3) one or more further monomers from the group consisting of the vinyl esters, vinyl ethers, acrylates, methacrylates, acrylamides and methacrylamides, and the amines (B) are selected from the group consisting of the(b.sub.1) cyclic amines of the general formula I ##STR1## and/or from the group consisting of the (b.sub.2) open-chain amines of the general formula II ##STR2## and/or from the group consisting of (b.sub.3) 1,4-thiazine, N,N',N"-trisvinylmelamine and N,N',N"-triallylmelamine, Z, R.sup.1, R.sup.2 and R.sup.3 having the meanings stated in the description.