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The prediction of both food intake and milk production constitutes a major issue in ruminants. This article presents a model predicting voluntary dry matter intake and milk production by lactating cows fed indoors. This model, with an extension to predict herbage intake at grazing presented in a second article, is used in the Grazemore decision support system. The model is largely based on the INRA fill unit system, consisting of predicting separately the intake capacity of the cows and the fill value (ingestibility) of each feed. The intake capacity model considers potential milk production as a key component of voluntary feed intake. This potential milk production represents the energy requirement of the mammary gland, adjusted by protein supply when the protein availability is limiting. Actual milk production is predicted from the potential milk production and from the nutritional status of the cow. The law of response of milk production is a function of the difference between energy demand and actual energy intake, modulated by protein intake level. The simulation of experimental data from different feeding trials illustrates the performance of the model. This new model enables dynamic simulations of intake and milk production sensitive to feeding management during the whole lactation period.