Biological invasions entail massive biodiversity losses and tremendouseconomic impacts that justify significant management efforts. Because thefunds available to control biological invasions are limited, there is a need toidentify priority species. This paper first review current invasive species pri-oritization methods and explicitly highlights their pitfalls. We then constructa cost-benefit optimization framework that incorporates species utility, eco-logical value, distinctiveness, and species interactions. This framework offersthe theoretical foundations of a simple and operational method for the man-agement of invasive species under a limited budget constraint. It takes theform of an algorithm for the prioritization of multiple biological invasions.