Crosslinkable, fluorine-containing copolymers, comprising:(a) 15 to 70 mol % of copolymerized units of a vinyl ester of the formula ##STR1## in which R.sup.1, R.sup.2 and R.sup.3 are branched or straight-chain alkyl radicals or cycloalkyl radicals, at most one of these radicals is hydrogen and at least one of these radicals is a methyl group, and where, furthermore, the entire acyl radical of the vinyl ester contains at least 9 and at most 28 carbon atoms,(b) 5 to 50 mol % of copolymerized units of a hydroxyalkyl vinyl ether of the formulaCH.sub.2 .dbd.CH--O--R.sup.4 --OH in which R.sup.4 OH is a branched or straight-chain hydroxy-alkyl group having 1 to 6 carbon atoms, and(c) copolymerized units of tertrafluoroethylene in an amount which makes up the sum of components (a) plus (b) plus (c) to 100, but with the proviso that at least 10 mol % of copolymerized units of tetrafluoroethylene are present in the copolymer.From these, highly weather-resistant surface-coating compositions are obtained on addition of crosslinking agents, solvents and conventional additives.