The extent of the potassium (K) limitation of forest productivity is probably more widespread than previously thought, and K limitation could influence the response of forests to future global changes. To understand the effects of K limitation on forest primary production, we have developed the first ecophysiological model simulating the K cycle and its interactions with the carbon (C) and water cycles. We focused on the limitation of the gross primary productivity (GPP) by K availability in tropical eucalypt plantations in Brazil. We used results from stand-scale fertilisation experiments as well as C flux measurements in two tropical eucalypt plantations to parameterise the model. The model was parameterised for fertilised conditions and then used to test for the effects of contrasting additions of K fertiliser. Simulations showed that K deficiency limits GPP by more than 50¿% during a 6-year rotation, a value in agreement with estimations in K-limited eucalypt stands. Simulations showed a decrease of modelled canopy transpiration of around 50¿% and a decrease in modelled water-use efficiency WUEGPP of 10¿%. Through a sensitivity analysis, we used the model to identify the most critical processes to consider when studying K limitation of GPP. The inputs of K to the stands, such as the atmospheric deposition and weathering fluxes, and the regulation of the cycle of K within the ecosystem were critical for the response of the system to K deficiency. Litter leaching processes were of lower importance, since residence time of K in litter was low. The new forest K-cycle model developed in the present study includes multiple K processes interacting with the carbon and water cycles, and strong feedbacks on GPP were outlined. This is a first step in identifying the source or sink limitation of forest growth by K.