In this report we describe a series of stepped Quaternary terraces on some piedmont tributaries of the Santa Cruz River valley in southeastern Arizona. These terraces began to form in early Pleistocene time, after major basin-and-range faulting ceased, with lateral planation of basin fill and deposition of thin fans of alluvium. At the end of this cycle of erosion and deposition, tributaries of the Santa Cruz River began the process of dissection and terrace formation that continues to the present. Vertical cutting alternated with periods of equilibrium, during which streams cut laterally and left thin deposits of channel fill. The distribution of terraces was mapped and compiled with adjacent mapping to produce a regional picture of piedmont stream history in the middle part of the Santa Cruz River valley. For selected tributaries, the thickness of terrace fill was measured, particle size and lithology of gravel were determined, and sedimentary features were photographed and described. Mapping of terrace stratigraphy revealed that on two tributaries, Madera Canyon Wash and Montosa Canyon Wash, stream piracy has played an important role in piedmont landscape development. On two other tributaries, Cottonwood Canyon Wash and Josephine Canyon Wash, rapid downcutting preempted piracy. Two types of terraces are recognized: erosional and depositional. Gravel in thin erosional terraces has Trask sorting coefficients and sedimentary structures typical of streamflood deposits, replete with bar-and-swale surface topography on young terraces. Erosional-terrace fill represents the channel fill of the stream that cuts the terrace; the thickness of the fill indicates the depth of channel scour. In contrast to erosional terraces, depositional terraces show evidence of repeated deposition and net aggradation, as indicated by their thickness (as much as 20+ m) and weakly bedded structure. Depositional terraces are common below mountain-front canyon mouths where streams drop their load in response to abrupt flattening of gradients and expansion of channel banks, and they extend down the piedmont along Josephine Canyon Wash. Gravel in depositional terraces also has sorting coefficients typical of streamflood deposits. Sedimentary features in both types of terraces are consistent with deposition by flash floods in ephemeral streams, suggesting the climate was arid. Bedding and clast armor are weakly developed, clast clusters and imbrication are common, and crossbedding is generally absent. Debris-flow deposits, even near the mountain front, are surprisingly rare. On the tectonically stable piedmont of southeastern Arizona, stream piracy and climate change are the most likely agents of terrace formation. Both piracy and climate change can cause rapid changes in discharge and sediment supply, which initiate cycles of incision, lateral cutting, and aggradation. Increased stream discharge initiates downcutting, but increased sediment supply interrupts downcutting and causes streams to cut laterally and aggrade. At times, on Madera Canyon Wash and Montosa Canyon Wash, stream piracy affected stream discharge and sediment supply, but on Cottonwood Canyon Wash and Josephine Canyon Wash, only climate change could have initiated terrace cutting. Terraces probably formed during extended arid intervals when sparse vegetation and flashy stream discharge combined to increase sediment supply. In most cases, sediment supply was sufficient to promote lateral cutting but not long-term aggradation. Thus, most streams formed erosional terraces. The middle Pleistocene Josephine Canyon Wash formed a depositional terrace because it had a source of abundant unconsolidated sediment.