A multilayer composite which has improved adhesion between the layers, comprising the following layers: I. an inner layer I selected from among a fluoropolymer molding composition and a polyolefin molding composition; II. a bonding layer II which has the following composition: a) from 2 to 80 parts by weight of a polyamine-polyamide graft copolymer, b) from 0 to 85 parts by weight of a polyester, c) from 0 to 85 parts by weight of a polymer selected from among polyamides, fluoropolymers and polyolefins, where the sum of the parts by weight of a), b) and c) is 100; d) not more than 50 parts by weight of additives; III. a layer III of a polyester molding composition.