A multilayer composite which comprises the following layers: I. an interior layer I selected from among a fluoropolymer molding composition and a polyolefin molding composition; II. a bonding agent layer II which has the following composition: a) from 0 to 80 parts by weight of a polyamine-polyamide graft copolymer, b) from 0 to 85 parts by weight of polyamide, c) from 0 to 85 parts by weight of a polymer selected from among fluoropolymers and polyolefins, with the sum of the parts by weight of a), b) and c) being 100, and, in addition, the sum of the components a) and b) comprising at least 20 parts by weight of monomer units derived from caprolactam and/or the combination hexamethylenediamine/adipic acid, hexamethylenediamine/suberic acid, hexamethylenediamine/sebacic acid, hexamethylenediamine/dodecanedioic acid, hexamethylenediamine/isophthalic acid or hexamethylenediamine/terephthalic acid and d) not more than 50 parts by weight of additives selected from among impact-modifying rubber and customary auxiliaries and additives; III. a layer III comprising an EVOH molding composition, has improved adhesion of the layers.