The 1991, M s = 7.0 Racha earthquake is the largest ever recorded in the Caucasus Mountains. Approximately three months after this thrust-faulting earthquake, a GPS network was set up to measure postseismic surface deformation. We present an analysis of these data, which indicate accelerated postseismic motions at several near-field sites. We model this deformation as either afterslip on the rupture surface or viscoelastic relaxation of the lower crust. We find that the postseismic motions are best explained by shallow afterslip on the earthquake rupture plane. The minimum postseismic moment release is estimated at 6.0 W 1018 N m, which is over 200 times the moment released by aftershocks in this same period and about 20% of the coseismic moment. We also show that the effective viscosity of the lower crust in the western Greater Caucasus region exceeds 1018 Pa s.