A process for preparing copolymer dispersions that includes subjecting A) one or more vinyl monomer mixtures containing a) OH-free (meth)acrylic esters and/or vinylaromatics, b) hydroxy-functional vinyl monomers and/or hydroxy-functional (meth)acrylic esters, c) ionic and/or potentially ionic monomers capable of free-radical copolymerization, and d)optionally further monomers, other than the compounds of components a) c), capable of free-radical copolymerization; to free-radical polymerization in the presence of e) compounds according to formula (I) ##STR00001## where R.sup.1 is an aliphatic, araliphatic or aromatic radical having 1 to 18 carbon atoms, R.sup.2 is H or CH.sub.3, R.sup.3, R.sup.4 are identical or different aliphatc radicals having 1 to 7 carbon atoms and n is 1 to 4; and subsequently dispersing the resultant copolymer B) before or after addition of a neutralizing agent C) in water. The resulting dispersions can be used to coat substrates.