The invention relates to a method for reacting polymers (A) comprising hydroxyl groups and which have repetitive structural units of general formula (I), wherein D represents a direct bond between the polymer backbone and a hydroxyl group, a C1- to C6-alkene group, a C5- to C12-arylene group, an oxyalkylene group of formula —O—R2—, an ester group of formula —C(O)—O—R2— or an amide group of formula —C(O)—N(R8)R2—, R2 represents a C2- to C10-alkene group, R8 represents hydrogen or an optionally substituted C2- to C10-alkyl group and n represents a number between 3 and 5000, with carboxylic acids B1) of formula (II) or carboxylic acid esters B2) of formula (III) R1—COOH (II) R1—COOR7 (III), wherein R1 represents a hydrocarbon group having 2 to 50 C atoms, and R7 represents a C1C4-alkyl group, in which the polymers (A); comprising the hydroxyl groups are exposed to microwaves in the presence of carboxylic acids of formula (II) or carboxylic acid esters of formula (III) and in the presence of water. The reaction mixture is heated to temperatures over 100° C. by microwave rays.