Sediment transport in mountain channels controls the evolution of mountainous terrain in response to climate and tectonics and presents major hazards to life and infrastructure worldwide. Despite its importance, we lack data on when sediment moves in steep channels and whether movement occurs by rivers or debris flows. We address this knowledge gap using laboratory experiments on initial sediment motion that cross the river to debris-flow sediment-transport transition. Results show that initial sediment motion by river processes requires heightened dimensionless bed shear stress (or critical Shields stress) with increasing channel-bed slope by as much as fivefold the conventional criterion established for lowland rivers. Beyond a threshold slope of ∼22°, the channel bed fails, initiating a debris flow prior to any fluvial transport, and the critical Shields stress within the debris-flow regime decreases with increasing channel-bed slope. Combining theories for both fluvial and debris-flow incipient transport results in a new phase space for sediment stability, with implications for predicting fluvial sediment transport rates, mitigating debris-flow hazards, and modeling channel form and landscape evolution.