A spherically symmetric Earth model with a viscoelastic mantle and an inviscid core is used to study the gravitational perturbation due to a lithospheric shear dislocation in the coseismic and postseismic regime. Our approach is based on a quasi-static solution of the equilibrium equations taking advantage of the normal mode technique for a layered incompressible Earth with linear viscoelastic rheology. We perform a systematic study of space and time evolution of gravity changes associated with a wide selection of seismic sources investigating the effects of several different mantle viscosity profiles. Our results show that the gravitational signal is sensitive not only to the viscosity of the asthenosphere but also to that of the mantle, including the portion below the 670 km discontinuity. As a case study, we compute the coseismic and postseismic gravity perturbation due to the 1964 Alaska earthquake. The last section is devoted to the analysis of the postseismic relaxation rates of the gravitational perturbation following that earthquake for several different viscosity profiles of the mantle. Our results show that experimental attempts to obtain reliable detection of static and quasi-static gravitational perturbation associated with seismic events would be of great importance in understanding the dynamic and viscosity profile of both upper and lower mantle. ¿ 1998 American Geophysical Union