The invention relates to a method for producing a hydroxy-aminopolymer, comprising the following steps: a) reacting at least one H-functional starter compound carrying at least one Zerewitinoff-active H-atom with an unsaturated cyclical carboxylic acid anhydride and at least one alkylene oxide compound in order to obtain a pre-polymer carrying hydroxyl groups; b) adding a primary amine and/or ammonia to the double bonds of the pre-polymer that carries hydroxyl groups obtained according to step a) in order to obtain the hydroxyl-aminopolymer, wherein the reaction of the H-functional starter compound with the unsaturated cyclical carboxylic acid and/or the addition of the alkylene oxide compound is carried out by using a double metal cyanide catalyst (DMC catalyst). The invention further relates to a hydroxyl aminopolymer that can be obtained according to the above-mentioned method, wherein the substance ratio between the alkylene oxide compound and the carboxylic acid anhydride is at least 1.1:1, and to the use of said hydroxyl-aminopolymer for producing a polyurethane urea polymer.