An optical waveguide having a core/sheath structure whose sheath comprises a polymer which is based on vinylidene fluoride and at least one other vinyl monomer containing fluorine and has been modified and crosslinked with a trisalkoxyvinylsilane, is suitable for transmission paths of ca. 10 to 100 m and can also be used at a temperature above 100.degree. C. without any significant reduction in the transmission path.