This research deals with the structural evolution of strike- slip fault zones as related to the statistics of earthquakes in those zones and the geometry of the fault traces. Significant results have already been obtained for the San Andreas fault in California and the Anatolian fault in Turkey. The work is to be extended to faults in the Mojave Desert in California and strike- slip faults in Japan. These ideas have not only yielded new physical insights into faulting but have important implications for earthquake hazard assessment. This research is a component of the National Earthquake Hazard Reduction Program.