A theory of Love waves propagating in a viscoelastic surface layer deposited on a perfect elastic substrate was considered. In the case of low losses(&ohgr;&eegr;44/&mgr;B0≪1)an analytical formula relating the attenuation coefficient of the Love wave and the viscoelastic parameters of the waveguide structure was established. This makes it possible to apply the obtained analytical formula in nondestructive testing for determining the rheological parameters of viscoelastic bodies. The established theory of Love waves in viscoelastic media can also be applied in seismology and integrated optics. ©1997 American Institute of Physics.