Recent investigations have shown that the extent of the channel network in some drainage basins is controlled by a threshold for overland flow erosion. The sensitivity of such basins to climate change is analyzed using a physically based model of drainage basin evolution. The GOLEM model simulates basin evolution under the action of weathering processes, hillslope transport, and fluvial bedrock erosion and sediment transport. Results from perturbation analyses reveal that the nature and timescale of basin response depends on the direction of change. An increase in runoff intensity (or a decrease in vegetation cover) will lead to a rapid expansion of the channel network, with the resulting increase in sediment supply initially generating aggradation along the main network, followed by downcutting as the sediment supply tapers off. By contrast, a decrease in runoff intensity (or an increase in the erosion threshold) will lead to a retraction of the active channel network and a much more gradual geomorphic response. Cyclic changes in runoff intensity are shown to produce aggradational-degradational cycles that resemble those observed in the field. Cyclic variations in runoff also lead to highly punctuated denudation rates, with denudation concentrated during periods of increasing runoff intensity and/or decreasing vegetation cover. The sediment yield from threshold-dominated basins may therefore exhibit significant variability in response to relatively subtle environmental changes, a finding which underscores the need for caution in interpreting modern sediment-yield data.