Conduit which can be used for an air or space vehicle fuel pipeline, the conduit comprising at least one multilayer pipe comprising a radially internal layer which is made of a thermoplastic material based on at least one thermoplastic polymer selected from the group consisting of polyamides, polyetherimides, phenylene polysulphides, polyetheretherketones (PEEK), polyetherketoneketones (PEKK) and mixtures thereof or made of a thermoplastic elastomer and which is sealed and chemically resistant to the fuel transported, and at least one reinforcing layer located radially above the internal layer, characterised in that the pipe has a curved and/or bent geometry, preferably three-dimensional, and in that the reinforcing layer is made of a composite material based on reinforcing means which are in close and direct contact with the underlying layer, such as the internal layer, said geometry being obtained according to one or other of the two following methods a) and b): a) the internal layer is hot-formed beforehand independently from the reinforcing layer to make it pass from an initial rectilinear geometry to this curved and/or bent geometry, said reinforcing means being selected from: i) based on at least one fibrous cylindrical braid impregnated with a thermosetting matrix, the reinforcing layer, forming a thermosetting composite with a thermosetting matrix of a cross-linking temperature less than the melting temperature of said underlying layer, or ii) reinforcing fibres intermixed with thermoplastic fibres or powders which are impregnated with a plastic polymeric coating which can be cross-linked chemically, the reinforcing layer forming, in these two cases, a thermoplastic composite with a thermoplastic matrix of transformation temperature less than that of said underlying layer; or b) the internal layer, in the initial rectilinear geometry thereof, is covered beforehand with the reinforcing layer wherein said reinforcing means are reinforcing fibres intermixed with a thermoplastic material in the form of fibres, of a film or powder, then this internal layer thus covered and softened is blast-moulded to confer the curved and/or bent geometry thereof to the pipe, the reinforcing layer obtained forming a thermoplastic matrix composite. a) the internal layer is hot-formed beforehand independently from the reinforcing layer to make it pass from an initial rectilinear geometry to this curved and/or bent geometry, said reinforcing means being selected from: i) based on at least one fibrous cylindrical braid impregnated with a thermosetting matrix, the reinforcing layer, forming a thermosetting composite with a thermosetting matrix of a cross-linking temperature less than the melting temperature of said underlying layer, or ii) reinforcing fibres intermixed with thermoplastic fibres or powders which are impregnated with a plastic polymeric coating which can be cross-linked chemically, the reinforcing layer forming, in these two cases, a thermoplastic composite with a thermoplastic matrix of transformation temperature less than that of said underlying layer; or i) based on at least one fibrous cylindrical braid impregnated with a thermosetting matrix, the reinforcing layer, forming a thermosetting composite with a thermosetting matrix of a cross-linking temperature less than the melting temperature of said underlying layer, or ii) reinforcing fibres intermixed with thermoplastic fibres or powders which are impregnated with a plastic polymeric coating which can be cross-linked chemically, the reinforcing layer forming, in these two cases, a thermoplastic composite with a thermoplastic matrix of transformation temperature less than that of said underlying layer; or b) the internal layer, in the initial rectilinear geometry thereof, is covered beforehand with the reinforcing layer wherein said reinforcing means are reinforcing fibres intermixed with a thermoplastic material in the form of fibres, of a film or powder, then this internal layer thus covered and softened is blast-moulded to confer the curved and/or bent geometry thereof to the pipe, the reinforcing layer obtained forming a thermoplastic matrix composite.