Abstract: The invention relates to the use of nondendrimeric, high-functionality hyperbranched polyesters and polycarbonates which are obtainable by reacting (i) at least one aliphatic, cycloaliphatic, araliphatic or aromatic dicarboxylic acid (A2) or derivatives thereof, or organic carbonates (A2?) with (ii) at least one x-hydric aliphatic, cycloaliphatic, araliphatic or aromatic alcohol (Cx) which has more than two OH groups, where x is a number greater than 2, preferably from 3 to 8, more preferably from 3 to 6, even more preferably from 3 to 4 and especially 3, and (iii) at least one fatty acid amide alkoxylate (D) of saturated or unsaturated C2-C30 fatty acid amides with an average of from 1 to 40 alkylene oxide units as demulsifiers for splitting crude oil emulsions.