The present invention is directed to a process for the preparation of polymers containing hydroxyl groups by reacting polymers based on acrylic acid and/or methacrylic acid and containing carboxyl groups with alkylene oxides in the presence of catalysts, characterized in that the catalysts used are(a) addition products containing two thioether groups of (i) mercaptoalkanols corresponding to the formula ##STR1## and (ii) doubly unsaturated terpene hydrocarbons and/or condensation products with a maximum molecular weight of 5000 obtained by the condensation of such addition products on their own or with other polyhydric alcohols having a molecular weight of 62 to about 200, and/or(b) relatively high molecular weight thioethers having a molecular weight of about 500 to 5000 obtainable by the condensation of thiodiglycols corresponding to the formula ##STR2## optionally in admixture with up to 50 hydroxyl equivalents percent, based on the total mixture, of other polyhydroxyl compounds having a molecular weight of 62 to about 200, in which formula, R and R' may be identical or different and denote hydrogen or a methyl group.The present invention is further directed to the use of the hydroxyl containing alkoxylation products obtained by this process as reactants for organic polyisocyanates (optionally blocked with blocking agents for isocyanate groups) in the production of polyurethane plastics, in particular high quality polyurethane coatings.