By analyzing body wave seismograms, we show that the rupture speed on the Main Kunlun Fault during the Mw 7.8 2001 Kunlunshan, Tibet, earthquake was highly variable and the rupture process consisted of three stages. In the first stage, the rupture accelerated from rest to an average speed of 3.3 km/s over a distance of 120 km. The rupture then propagated for another 150 km at an apparent rupture speed exceeding the P wave speed. In the final stage, the earthquake fault bifurcates, and the rupture front slowed down. The region of highest rupture velocity is found to coincide with the region of highest fault slip, has the longest slip duration, and is where off-fault ground cracking is observed in the field. Stress drops are found to be higher in regions of higher rupture speeds. The greatest concentration of aftershocks is located near the fault bifurcation zone and hence coincides with the region of highest fault slip, highest stress drop and highest rupture velocity. The fault width is no more than 10 km in most places and is about 20 km in the region of highest slip. This narrow fault width is attributed to the fact that crust below this depth is sufficiently warm not to permit brittle failure to occur. The remarkable similarity of this earthquake with the 1906 California earthquake, in spite of occurring in very different tectonic regimes, is discussed.