The present invention relates to triazine-containing organosilicon compounds having units of the formulaA.sub.a R.sub.b X.sub.c SiO.sub.(4-a-b-c)/2 (I),whereR is identical or different and denotes a hydrogen atom or a monovalent substituted or unsubstituted hydrocarbon radical, having 1 to 26 carbon atoms, preferably 1 to 18 per radical,X is identical or different and is a halogen atom, a chlorine atom or a radical of the formula --OR.sup.1, where R.sup.1 denotes an alkyl radical, having 1 to 18 carbon atoms, preferably 1 to 8 per radical and which may be substituted by an ether oxygen atom,a is 0 or 1, preferably 0.01-0.5b is 0, 1, 2 or 3, preferably 0.5-3.0c is 0, 1, 2 or 3, preferably 0.0-2.0 and the sum a+b+c.ltoreq.4, preferably 0.1-3.5, andA is a radical of the formula ##STR1## where R.sup.2 is an unbranched or branched, optionally substituted alkylene radical, having 1 to 18, preferably 1 to 12, carbon atoms,Y is identical or different and denotes a hydrogen atom or an unbranched or branched alkyl radical, having 1 to 12, preferably 1 to 8, carbon atoms or denotes a radical of the formula --OR.sup.1, where R.sup.1 has the meaning given above, andZ is identical or different and denotes X, --NR.sub.2, --(O)CR or --SR, where X and R have the meanings given above with the proviso that at least one radical A containing at least one halogen atom, preferably a chlorine atom, is present per polymer molecule.