By means of a spherical Earth model with Maxwell rheology we compute the coseismic and the postseismic displacements associated with the June 9, 1994 Bolivia earthquake. Our results are compared with the coseismic uplift detected by an array of broadband seismic stations in Southern Bolivia and with previous theoretical predictions. Our solution method has been recently employed to study the global deformations due to large lithospheric earthquakes. In contrast to purely elastic Earth models, our method includes the time-dependent effects associated with mantle relaxation. The results presented here show that the surface deformation due to a deep-focus earthquake are sensibly magnified by the delayed viscoelastic mantle relaxation. The time-scales which characterize mantle relaxation and the time evolution of surface observables depend on the rheological profile of the upper mantle, and particularly on the thickness of the viscoelastic asthenosphere. ¿ 1997 American Geophysical Union