AbstractFluvial aggradation and incision are often linked to Quaternary climate cycles, but it usually remains unclear whether variations in runoff or sediment supply or both drive channel response to climate variability. Here we quantify sediment supply with paleo‐denudation rates and provide geochronological constraints on aggradation and incision from the Sfakia and Elafonisi alluvial‐fan sequences in Crete, Greece. We report seven optically stimulated luminescence and ten radiocarbon ages, eight10Be and eight36Cl denudation rates from modern channel and terrace sediments. For five samples,10Be and36Cl were measured on the same sample by measuring10Be on chert and36Cl on calcite. Results indicate relatively steady denudation rates throughout the past 80 kyr, but the aggradation and incision history indicates a link with climate shifts. At the Elafonisi fan, we identify four periods of aggradation coinciding with Marine Isotope Stages (MIS) 2, 4, 5a/b, and likely 6, and three periods of incision coinciding with MIS 1, 3, and likely 5e. At the Sfakia fan, rapid aggradation occurred during MIS 2 and 4, followed by incision during MIS 1. Nearby climate and vegetation records show that MIS 2, 4, and 6 stadials were characterized by cold and dry climates with sparse vegetation, whereas forest cover and more humid conditions prevailed during MIS 1, 3, and 5. Our data thus suggest that past changes in climate had little effect on landscape‐wide denudation rates but exerted a strong control on the aggradation–incision behaviour of alluvial channels on Crete. During glacial stages, we attribute aggradation to hillslope sediment release promoted by reduced vegetation cover and decreased runoff; conversely, incision occurred during relatively warm and wet stages due to increased runoff. In this landscape, past hydroclimate variations outcompeted changes in sediment supply as the primary driver of alluvial deposition and incision.