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A summary is given of properties of Love and Rayleigh waves in stratified isotropic media. The study of propagation of such waves in anisotropic and piezoelectric media, carried out in view of obtaining "pure" modes, shows that two modes can be "pure" and only one of them at a time can be piezoelectrically stiffened. The Rayleigh wave is stiffened if the sagittal plane is a plane of symmetry whereas the Love wave is stiffened if the perpendicular to the sagittal plane is a binary axis. The problems in devising dispersive delay lines using these waves are discussed and the pairs of materials which seem to be the most interesting ones are given together with the different excitation methods and expected performance of these delay lines relating to large bandwidths and high compression ratios. The results of experiments carried out with Love and Rayleigh waves excited by ceramic transducers directly bonded onto the layer show that the total untuned insertion losses can be less than 20 dB with a 2.5-MHz bandwidth and less than 50 dB with a 100-MHz bandwidth. Also described is the performance of a delay line whose time delay variation is nearly 8 µs with a 30-MHz bandwidth, the central frequency being 32.5 MHz.