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Abstract Chemical erosion is of wide interest due to its influence on topography, nutrient supply to streams and soils, sediment composition, and Earth's climate. While controls on chemical erosion rate have been studied extensively in steady‐state models, few studies have explored the controls on chemical erosion rate during transient responses to external perturbations. Here we develop a numerical model for the coevolution of soil‐mantled topography, soil thickness, and soil mineralogy, and we use it to simulate responses to step changes in rates of rock uplift, soil production, soil transport, and mineral dissolution. These simulations suggest that tectonic and climatic perturbations can generate responses in soil chemical erosion rate that differ in speed, magnitude, and spatial pattern and that climatic and tectonic perturbations may impart distinct signatures on hillslope mass fluxes, soil chemistry, and sediment composition. The response time of chemical erosion rate is dominantly controlled by hillslope length and is secondarily modulated by rates of rock uplift, soil production, transport, and mineral dissolution. This strong dependence on drainage density implies that a landscape's chemical erosion response should depend on the relative efficiencies of river incision and soil transport and thus may be mediated by climatic and biological factors. The simulations further suggest that the timescale of the hillslope response may be long relative to that of river channel profiles, implying that chemical erosion response times may be limited more by the sluggishness of the hillslopes than by the rate of signal propagation through river channel profiles.