Sustainable management of natural resources, and in particular fisheries, must take into account several conflicting objectives. This is the case in the French Guiana shrimp fishery for which profitability objectives imply a reduction in the fishing activity. On the one hand, this fishery has negative externalities on marine biodiversity due to discards. On the other hand, this fishery has positive externalities on the economy of the local community and interestingly enough on a protected seabird species in the area (the Frigatebird that feeds on discards). In this paper, we examine the viability of that system considering two sustainability objectives: an economic objective in terms of the profitability of the fishing activity, and a conservation objective in terms of the Frigatebird population. For that purpose, we have developed a dynamic model of that bioeconomic system and study here the trade-offs between the two conflicting objectives. It provides a means to quantify the necessary give and takes involving the economic and ecological objectives that would ensure a viable management solution. Our study confirms the relevance of the viability approach to address natural resource management issues, which should lead to the development of new tools for the arbitration of conflicting sustainability, objectives. In particular, such tools could be used as a quantitative basis for cost-benefit analysis taking into account environmental externalities. (C) 2009 Elsevier B.V. All rights reserved.