Hyperbranched polycarbonates having stabilizing groups, prepared by reaction of (a) at least one compound having at least three alcoholic hydroxyl groups per molecule with (b) at least one reagent of the general formula I (c) and at least one reagent of the general formula X3-(A1)m-X4, where the variables are defined as follows: X1, X2 are identical or different and are selected from among halogen, C1-C10-alkoxy, C6-C10-aryloxy and O—C(═O)-halogen, X3 is a functional group selected from among OH, SH, NH2, NH—C1-C4-alkyl, iso-cyanate, epoxy, COOH, COOR12, C(═O)—O—C(═O), C(═O)—Cl, R12 is C1-C4-alkyl or C6-C10-aryl, A1 is a spacer or a single bond, m is zero or one. X4 is a group selected from among phenol groups, benzophenones, aromatic amines and nitrogen-comprising heterocycles, in each case substituted or unsubstituted.