This paper presents a dynamic principal-agent model of aquatic species invasions in which a manager, concerned about the spread of invasive species across lakes by boaters, sets interseasonal management controls on a lake-by-lake basis, and boaters make a series of intraseasonal trip decisions to maximize random utility during the course of the season, conditional on the controls imposed by the manager. The results of a simulated invasion of Eurasian watermilfoil (Myriophyllum spicatum) highlight interesting aspects of the optimal management policies under two different management objectives: maximizing boater welfare and minimizing milfoil spread.