We use Global Positioning System (GPS) measurements across the Xidatan segment of the Kunlun fault in the Tibetan Plateau to investigate the surface deformation following the 2001 Mw 7.8 Kokoxili earthquake. We find significant post-seismic deformation during the period 2007-2015, characterized by an asymmetric shear across the 2001 rupture, with average velocities reaching ~10 mm/yr about 30-45 km south of the coseismic rupture. We also find that the postseismic transients diffused away from the coseismic rupture through time, with a shift of the maximum transient rates from ~20-30 km south of the rupture in 2001-2002 to ~30-45 km in 2007-2015. Viscoelastic relaxation is the dominant physical process during the period 2007-2015. The estimated effective viscosity of the lower crust beneath the Songpan-Ganzi terrane is 2×1018-3×1018 Pa s from the 2001-2002 data, and it has increased to ~2×1019 Pa s for the period 6 to 14 years after the event. The large asymmetry in the postseismic deformation field indicates a laterally heterogeneous lower crust beneath the northern Tibetan Plateau. Viscoelastic relaxation models show that the viscosity of the lower crust beneath the Qaidam basin is ~2 and ~4 times larger than the viscosity of the lower crust beneath the Songpan-Ganzi terrane in 2001-2002 and 2007-2015, respectively. Based on these data and results from previous studies, we postulate that the Kunlun fault itself is not the unique rheological boundary and that additional domains with viscosity increasing from the Qiangtang terrane to the Qaidam basin appear to be required.