The invention relates to a method to produce a modified hyperbranched polyesteramide, containing at least two β-hydroxylamide ester groups and optionally also a hydroxyalkylamide endgroup, wherein (a) a hydroxy-, or aminefunctional monomer, oligomer or polymer is contacted with a first molar excess of a cyclic carboxylic acid anhydride, forming a mixture of an acid functional ester, respectively an acid functional amide and a cyclic carboxylic acid anhydride; (b) the mixture is contacted with an amount of alkanediolamine, wherein the amount is a second molar excess with respect to the first molar excess. The invention further relates to a modified hyperbranched polyesteramide containing at least two β-hydroxylamide ester groups and optionally also a hydroxyalkylamide endgroup with a degree of polymerisation of more than 19, as well as the use of these polyesteramides as rheology modifier in gas-oil or in diesel.