Interpolymers of aromatic polyesters and cross-linked (or partially cross-linked) rubbers and a process for their production in which a mixture of a cross-linked rubber in latex form containing reactive groups and an aqueous solution of an alkali metal or alkaline earth metal diphenolate is reacted with a solution of a dicarboxylic acid halide and/or a carbonyl halide in a water-immiscible solvent so that an aromatic polyester forms at the water/organic solvent phase boundary, which polyester goes over into the organic phase and the rubber at the same time also goes into the organic phase. The interpolymer of rubber and organic polyester thus formed is suitable for the production of moulded articles of all kinds by the methods of thermoplastic shaping such as extrusion and injection moulding.