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To represent the impact of grazing livestock on carbon (C) and nitrogen (N) dynamics in grasslands, we implement a livestock module into LPJmL5.0-tillage, a global vegetation and crop model with explicit representation of managed grasslands and pastures, forming LPJmL5.0-grazing. The livestock module uses lactating dairy cows as a generic representation of grazing livestock. The new module explicitly accounts for forage quality in terms of dry-matter intake and digestibility using relationships derived from compositional analyses for different forages. Partitioning of N into milk, feces, and urine as simulated by the new livestock module shows very good agreement with observation-based relationships reported in the literature. Modelled C and N dynamics depend on forage quality (C:N ratios in grazed biomass), forage quantity, livestock densities, manure or fertilizer inputs, soil, atmospheric CO2 concentrations, and climate conditions. Due to the many interacting relationships, C sequestration, GHG emissions, N losses, and livestock productivity show substantial variation in space and across livestock densities. The improved LPJmL5.0-grazing model can now assess the effects of livestock grazing on C and N stocks and fluxes in grasslands. It can also provide insights about the spatio-temporal variability of grassland productivity and about the trade-offs between livestock production and environmental impacts.