The land modeling community has recognized that there are substantial nutrient limitation effects on the global terrestrial carbon cycle over the past several decades, and many modeling groups have been making large investments to incorporate nutrient sub-models within their carbon cycle models. These implementations of nutrient limitation concepts are very diverse, from simple empirical down-regulation of potential Gross Primary Productivity (GPP) under nutrient deficit conditions to a more mechanistic consideration of direct nutrient constraints on ecosystem functioning. In this study, we introduce a new approach, based on the Equilibrium Chemistry Approximation, to model nitrogen and phosphorus limitations in ALMv1 (the ACME Land Model). This development is one of the two approaches being developed and analyzed for the Coupled BGC Experiment. The development is rigorously grounded on (1) recent theoretical advances in understanding multiple-consumer, multiple-nutrient competition; (2) a generic dynamic allocation scheme based on water, nitrogen, phosphorus, and light availability; (3) prognostic treatment of nutrient constraints on C dynamics; and (4) global datasets of plant physiology traits. Through benchmarking the model against global plant and soil carbon pools and fluxes using the ILAMB package, we show that our implementation of nutrient constraints on the terrestrial carbon cycle improves predictions compared to the baseline models and is robust at the global scale.