The present invention relates to novel polymer compositions, to a process for their manufacturing, to the use of said polymer compositions for modifying the viscosity of aqueous compositions, and to water-borne coating compositions containing the novel polymer compositions as thickeners. The polymer compositions comprise a polymer material which is obtainable by reacting: a) a polymer P1 having at least one functional group of the formula (I), where k is an integer from 0 to 4; n is 0 or 1 p is an integer from 1 to 10, the number average of p being from 1.5 to 10; Q is a divalent moiety selected from the group consisting of —O— and —NH—; P is a p-valent hydrophilic neutral polymer radical; and R1 is as defined in the claims; with b) a succinic anhydride of the formula (II) where R is C4-C24-alkyl or C4-C24-alkenyl.