The availability of phosphorus (P) and nitrogen (N) constrains the ability of ecosystems to use resources such as light, water and carbon. In turn, nutrients impact the distribution of productivity, ecosystem carbon turnovers and their net exchange of CO2 with the atmosphere in response to variation of environmental conditions in both space and time. In this study, we evaluated the performance of the global version of the land surface model ORCHIDEE-CNP (v1.2), which explicitly simulates N and P biogeochemistry in terrestrial ecosystems coupled with carbon, water and energy transfers. We used data from remote sensing, ground-based measurement networks and ecological databases. Components of the N and P cycle at different levels of aggregation (from local to global) are in good agreement with data-driven estimates. When integrated for the period 1850 to 2017 forced with variable climate, rising CO2 and land use change, we show that ORCHIDEE-CNP underestimates the land carbon sink in the Northern Hemisphere (NH) during recent decades despite an a priori realistic gross primary productivity (GPP) response to rising CO2. This result suggests either that processes other than CO2 fertilization, which are omitted in ORCHIDEE-CNP such as changes in biomass turnover, are predominant drivers of the northern land sink and/or that the model parameterizations produce emerging nutrient limitations on biomass growth that are too strict in northern areas. In line with the latter, we identified biases in the simulated large-scale patterns of leaf and soil stoichiometry as well as plant P use efficiency, pointing towards P limitations that are too severe towards the poles. Based on our analysis of ecosystem resource use efficiencies and nutrient cycling, we propose ways to address the model biases by giving priority to better representing processes of soil organic P mineralization and soil inorganic P transformation, followed by refining the biomass production efficiency under increasing atmospheric CO2, phenology dynamics and canopy light absorption.