We study the global viscoelastic deformations associated with a shear dislocation on a fault embedded in a viscoelastic mantle. To address this problem, we extend the theory of the quasi-static deformations of a Maxwell, spherical, N-layer incompressible Earth, previously limited to the modeling of the effects of earthquakes occurring only within the elastic lithosphere. Permanent postseismic deformations, which can be generated by lithospheric sources, cannot be sustained if the source region is viscoelastic; however, the transient response of the mantle strongly depends on the viscosity of the source region. We use the technique developed here to investigate thoroughly the quasi-static surface deformations induced by seismic events of variable depth. We show that owing to the combined effect of sphericity and viscoelastic mantle relaxation, the surface displacements do not systematically decrease as the depth of the source increases. Instead, with increasing source depth we predict an increasing efficiency of mantle relaxation in triggering postseismic deformations of large size. Most of our results are based on a simple four-layer model, with a 100-km-thick lithosphere, upper and lower mantle separated by the 670-km discontinuity, and a fluid core; the last part of this work is devoted to a study of the effects of a low-viscosity asthenosphere on the rates of deformation detected at the Earth's surface. The findings reported here may be useful for the interpretation of the transient motions of the Earth's surface in response to deep-focus earthquakes. ¿ 2000 American Geophysical Union