The nature of slope acquisition by alluvial fans was studied by comparing the slope evolution of 37 tributary fans to the San Juan River in an arid region of western Argentina. Each of these fans is characterized by truncation of the distal end as a result of incision by the San Juan River. The alluvial-fan slope prior to incision and the slope of the active channel for each fan was measured. River accumulation terraces indicate that fan incision was probably synchronous along the valley. Incised channels in each fan evolved over the same interval, but they show different degrees of advance of erosion. Values of old fan slope fit well with known power laws relating them to drainage area (r = 0.865). Slopes of incised channels also fit with power laws, but with a lower regression coefficient (r 5 0.741). The regression lines in each case have almost the same slope (0.218, sd 5 0.02, and 0.215, sd 5 0.03, respectively), which suggests that, although the incised-channel slope is not an equilibrium feature, both the original and the secondary fans follow the same law of variation. An explanation for this phenomenon is that the transport efficiency of the fans may be related to the size of the basin. If mean runoff and peak floods are roughly regulated by drainage area, fan slopes of larger drainage basins will evolve faster than those of smaller basins. Apparently, as a group of fans approach an equilibrated state, their slopes become distributed along successive parallel regression lines, progressively displaced upward in the diagram, as long as climatic conditions remain constant. To see the effects of water availability on fan slope, we also compared slopes and drainage-basin areas of fans located in settings with different specific runoff, which is approximately a function of annual rainfall. The regression lines for each set of alluvial fans are roughly parallel. The smaller intercept value for humid fans indicates that for a given drainage area, fans in arid settings are steeper than those in more humid settings. Fans dominated by mud flows and dilute flash floods were plotted together, but no major differences were observed in this general behavior. This suggests that the steepness of a fan is not primarily related to compositional factors or to the sediment transport process, but to transport efficiency. Episodic-flood fans of Argentina show slopes comparable to the "mudflow" fans of Death Valley because water supply and therefore transport efficiency are similar. Drainage-basin area combined with mean annual rainfall may largely determine transport efficiency, by controlling mean runoff across the fan. As a result, transport efficiency may define not only alluvial-fan slope but also the rate at which the alluvial-fan slope reestablishes equilibrium after some external change.