Increasing nutrient circularity and use efficiency is a leading topic in the search for more sustainable agri-food-waste systems (AFWS). This paper proposes a method to assess the role of crops and livestock in nutrient circularity and use efficiency in an AFWS. The method is based on the analysis of nutrient flows, a detailed typology of flows, and a set of 3 groups of indicators to characterize (i) circularity between sub-systems, (ii) the process efficiency of the sub-systems and (iii) the efficiency of the AFWS. The method is illustrated using the nitrogen metabolism of the AFWS of a tropical Island, French Reunion Island. The island's current nitrogen use efficiency is very low (0.7%). Crops and livestock are major sources of inefficiencies due to their processes, they account for respectively, 42% and 9% of total AFWS inefficiency. However, crops and livestock are involved in circularity, as they play, respectively, a recycling receiver and recycling supplier role. Among the internal recycling routes between all sub-systems, 41% go to crops and 31% come from livestock. The paper argues that circularity and process efficiency are not objectives per se but means to achieve AFWS efficiency, and that the distinction between these three elements enable a systemic multi-level understanding of the roles of crops and livestock.