The present invention relates to a process for the production of polyhydroxyl compounds having a hydroxyl group content of 2 to 10% by weight and a viscosity at 23.degree. C. of 250 to 80,000 mPa.s by the radically initiated polymerization at a reaction temperature of 80.degree. to 220.degree. C. ofa) 100 parts by weight of a mixture of olefinically unsaturated monomers containing at least 1% by weight of monomers containing alcoholic hydroxyl groups in the presence ofb) 5 to 500 total parts by weight, which may be present at the beginning of the reaction or added during the reaction, of one or more cyclic compounds which, in the presence of initiator compounds containing alcoholic hydroxyl groups, are capable of a ring-opening polymerization reaction andc) 2 to 300 parts by weight, which may be present at the beginning of the reaction or added during the reaction, of one or more polyhydric alcohols having a molecular weight of 62 to 1000.The present invention also relates to the polyhydroxyl compounds obtained by this process and to their use in combination with suitable hardeners as binders for one-component or two-component coating compositions.