The Rio Grande in the Big Bend region of Texas, USA, and Chihuahua and Coahuila, Mexico, undergoes rapid geomorphic changes as a result of its large sediment supply and variable hydrology; thus, it is a useful natural laboratory to investigate the relative importance of flow strength and sediment supply in controlling alluvial channel change. We analyzed a suite of sediment transport and geomorphic data to determine the cumulative influence of different flood types on changing channel form. In this study, physically based analyses suggest that channel change in the Rio Grande is controlled by both changes in flow strength and sediment supply over different spatial and temporal scales. Channel narrowing is primarily caused by substantial deposition of sediment supplied to the Rio Grande during tributary-sourced flash floods. Tributary floods have large suspended-sediment concentrations, occur for short durations, and attenuate rapidly downstream in the Rio Grande, depositing much of their sediment in downstream reaches. Long-duration floods on the mainstem have the capacity to enlarge the Rio Grande, and these floods, released from upstream dams, can either erode or deposit sediment in the Rio Grande depending upon the antecedent in-channel sediment supply and the magnitude and duration of the flood. Geomorphic and sediment transport analyses show that the locations and rates of sand erosion and deposition during long-duration floods are most strongly controlled by spatial changes in flow strength, largely through changes in channel slope. However, spatial differences in the in-channel sediment supply regulate sediment evacuation or accumulation over time in long reaches (greater than a kilometer).