The invention relates to the use of nondendrimeric, highly functional, hyperbranched polymers as demulsifiers for breaking crude oil emulsions. The hyperbranched polymers are preferably hyperbranched polycarbonates, hyperbranched polyesters, hyperbranched polyethers, hyperbranched polyurethanes, hyperbranched polyureapolyurethanes, hyperbranched polyureas, hyperbranched polyamides, hyperbranched polyetheramines and hyperbranched polyesteramides which are functional groups selected from the group consisting of —OC(O)OR, —COOH, —COOR, —CONHR, —CONH2, —OH, —SH, —NH2, —NHR, —NR2, —SO3H, —SO3R, —NHCOOR, —NHCONH2 and —NHCONHR, where R is an optionally substituted alkyl or aryl radical.