The exponents in downstream hydraulic geometry relations are commonly interpreted as indices of the rates of downstream change in flow width, depth, and velocity. These downstream rates of change reflect the nature of channel adjustment to increasing drainage area and discharge. The most common values of the exponents are 0.5 for width, 0.4 for depth, and 0.1 for velocity, although a range of values have been recorded for various rivers. We compare downstream hydraulic geometry relations for two channel networks in hydroclimatically extreme regions; ephemeral Yuma Wash (186 km²) in southwestern Arizona and the Chena River (5540 km²) in central Alaska. Both basins have flashy hydrologic regimes. Yuma Wash has minimal vegetation and soil development, and abundant surface runoff during rainstorms. The forested Chena basin has channel banks with an upper layer of fine sediment; is underlain by permafrost; and has steeply sloping flow duration curves indicative of relatively low baseflow and subsurface storage. We hypothesized that, relative to average river values, width would increase more rapidly downstream along both channels because of flashy discharge and erodible banks. This hypothesis was supported by the Yuma Wash data (width 0.78, depth 0.15, velocity 0.14), but not by the Chena data (w 0.41, d 0.23, v 0.38). Yuma Wash exhibits the lower downstream increase in depth and greater downstream increase in width and velocity which have been described for other arid-region rivers. The meandering Chena River apparently has sufficient bank cohesion as a result of silt-clay content, vegetation and permafrost, to have a lower rate of downstream increase in width. We interpret the relatively smaller incrase in depth along the Chena to reflect a resistant cobble bed which limits scour, and extensive overbank flow during high discharges. The relatively larger increase in velocity may reflect a downstream increase in suspended-sediment concentration during high flows, and consequent dampening effect on turbulence. These results suggest that different types of hydroclimatically extreme environments may have substantially different types of downstream hydraulic geometry because of factors other than discharge variability.