The invention relates to a process for the preparation of a polyurethane polymer, comprising the step of reaction of A) polyester polyols with secondary hydroxyl end groups, which are obtainable from the reaction of a polyester comprising carboxyl end groups with an epoxide of the general formula (1): wherein R1 represents an alkyl radical or an aryl radical and wherein the polyester comprising carboxyl end groups has an acid number of from ≧25 mg of KOH/g to ≦̸400 mg of KOH/g and a hydroxyl number of ≦̸5 mg of KOH/g, with B) polyisocyanates which are chosen from the group comprising toluoylene-diisocyanate, diphenylmethane-diisocyanate, polymeric diphenylmethane-diisocyanate, xylylene-diisocyanate, naphthylene-diisocyanate, hexamethylene-diisocyanate, diisocyanatodicyclohexylmethane and/or isophorone-diisocyanate. The invention furthermore relates to polyurethane polymers prepared by such a process.