The invention relates to polymers carrying ester/hydroxyl groups, containing repetitive structural units of formulae (I) and (II) in a block-wise, alternating or statistical sequence, wherein D represents a direct bond between the polymer backbone and the hydroxyl group, a C1- to C6-alkene group, a C5- to C12-arylene group, an oxyalkene group of formula —O—R2—, an ester group of formula —C(O)—O—R2— or an amide group of formula —C(O)—N(R3)R2—, E represents a hydrocarbon group having 1 to 50 C-atoms, R2 represents a C2- to C10-alkene group, R3 represents hydrogen or a C1- to C10-alkyl group, which can carry substituents, k represents a number between 1 and 1000, n represents a number from 0 to 4999, m represents a number from 1 to 5000, and n+m represents a number between 10 to 5000, under the proviso that a) the molar portion of the structural units (I); on the polymer is between 0 and 99.9 mol-%, and b) the molar portion of the structural units (II) on the polymer is between 0.1 and 100 mol-% of the repetitive units. The invention also relates to a method for the production of said polymers using microwaves.