Geomorphic and Quaternary geologic studies provide data with which to assess seismic hazard in southeastern Arizona and adjacent New Mexico and Sonora, Mexico, where one large (M ~ 7 1/4) historic earthquake has occurred against a background of very low seismicity. Conclusions regarding the distribution and timing of late Quaternary faulting are based on (1) estimated ages of soils based on correlation with soils near Las Cruces in southern New Mexico; (2) use of surface age-fault offset relationships to constrain the age of most-recent fault movement and to estimate the frequency of movement along individual faults; and (3) morphologic analyses of fault scarps to estimate their ages. Individual late Quaternary faults in the region have surface rupture recurrence intervals on the order of 105 years. However, the major earthquake that occurred in 1887 in northeastern Sonora is evidently part of a series of 5 or 6 surface-rupturing earthquakes that have occurred since 20 ka in a N-S-trending zone straddling the Arizona-New Mexico border. Surface ruptures during the late Pleistocene (about 20-120 ka) occurred from near Tucson east to the border area, but the rate of surface rupture occurrence was evidently 4-25 times lower than during the past 20 kyo The rate of Holocenelatest Pleistocene surface-rupturing, while much lower than some portions of the northern Basin and Range province, evidently represents a burst of activity relative to the average long-term rate of faulting in southern Arizona.