AbstractAlluvial rivers aggrade, incise, and adjust their sediment‐transport rates in response to changing sediment and water supply. Fluvial landforms, such as river terraces, and downstream stratigraphic archives may therefore record information about past environmental change. Using a physically based model describing sediment transport and long‐profile evolution of alluvial rivers, we explore how their responses to environmental change depend on distance downstream, forcing timescales, and whether sediment or water supply is varied. We show that amplitudes of aggradation and incision, and therefore the likelihood of terrace formation, are greater upstream and in shorter and/or wetter catchments. Aggradation and incision, and therefore terrace ages, may also lag behind environmental change. How sediment‐transport rates evolve depends strongly on whether water or sediment supply is varied. Diverse responses to environmental change could arise in natural alluvial valleys, controlled by their geometry and hydrology, with important implications for paleo‐environmental interpretations of fluvial archives.