We study coseismic and postseismic stress fields caused by a normal faulting earthquake in a self-gravitating, stratified, viscoelastic spherical Earth over distances from a few to hundreds of kilometers. We investigate the contribution of postseismic relaxation on the induced Coulomb stress for extensional tectonic settings accounting for the effects of the Earth stratification. We use a numerical code based on the spherical self-gravitating Earth model developed by Piersanti et al. <1995, 1997>. We study how postseismic relaxation can modify the state of stress at the base of the seismogenic layer where large earthquakes are believed to nucleate. We compare our results with those obtained by means of a three-dimensional dislocation model in an elastic half-space, which does not account for the time-dependent postseismic stress transfer. The viscoelastic relaxation process modifies the coseismic stress changes during time periods from several decades to centuries. The postseismic stress is generally greater than the coseismic stress change. Postseismic relaxation increases the Coulomb stress near the causative faults and tends to reduce the stress shadow areas. The temporal evolution of Coulomb stress reveals that in addition to the viscosity value, the thickness of the elastic layer controls the time at which the relaxation process is completed. A larger thickness of the elastic layer yields a faster relaxation in the first few decades after the seismic event but smaller postseismic stress amplitudes at longer timescales. One of the most significant results of this study is the extreme sensitivity of the timescales of the viscoelastic relaxation to small changes in the thickness and depth of the shallowest viscoelastic layer as well as in variation of the viscosity. Such a result suggests that the interpretation of the time evolution of the postseismic signals only in terms of viscosity values could lead to misleading conclusions. ¿ 2001 American Geophysical Union