A flexible pipe of multilayer structure with unbonded layers, where the pipe has an interior lining which comprises the following layers: a) at least one layer of which the material is composed of a moulding composition based on a polymer selected from the group of: polyarylene ether ketone, polyphenyl sulphone, polyphenylene sulphide, polyarylene ether ketone/polyphenylene sulphide blend and semiaromatic polyamide, where from 5 to 100 mol % of the dicarboxylic acid content thereof derives from an aromatic dicarboxylic acid having from 8 to 22 carbon atoms, and which has a crystallite melting point Tm of at least 260° C.; b) at least one layer of which the material is composed of a fluoropolymer moulding composition can be operated at temperatures above 130° C. The pipe has particular suitability for offshore applications in the production of oil or of gas.