The period equation for Love waves is derived for a layered medium, which is composed of a compressible, viscous liquid layer sandwiched between homogeneous, isotropic, elastic solid layer and homogeneous, isotropic half space. In general, the period equation will admit complex roots and hence Love waves will be dispersive and attenuated for this type of model. The period equation is discussed in the limiting case when thicknessH 2 and coefficient of viscosity, η2, of the liquid layer tend to zero so as to maintain the ratioP=H 2/η2 constant. Numerical values for phase velocity, group velocity, quality factor (Q) and displacement in the elastic layer and half space have been computed as a function of the frequency for first and second modes for various values of the parameterP. It is shown that Love waves are not attenuated whenP=0 and ∞. The computed values ofQ for first and second modes indicate that whenP≠0 or ∞ the value ofQ attains minimum value as a function of dimensionless angular frequency.