Suppression of the invasive plant Salvinia molesta by the salvinia weevil is an iconic example of successful biological control. However, in the billabongs (oxbow lakes) of Kakadu National Park, Australia, control is fitful and incomplete. By fitting a process-based nonlinear model to thirteen-year data sets from four billabongs, here we show that incomplete control can be explained by alternative stable states--one state in which salvinia is suppressed and the other in which salvinia escapes weevil control. The shifts between states are associated with annual flooding events. In some years, high water flow reduces weevil populations, allowing the shift from a controlled to an uncontrolled state; in other years, benign conditions for weevils promote the return shift to the controlled state. In most described ecological examples, transitions between alternative stable states are relatively rare, facilitated by slow-moving environmental changes, such as accumulated nutrient loading or climate change. The billabongs of Kakadu give a different manifestation of alternative stable states that generate complex and seemingly unpredictable dynamics. Because shifts between alternative stable states are stochastic, they present a potential management strategy to maximize effective biological control: when the domain of attraction to the state of salvinia control is approached, augmentation of the weevil population or reduction of the salvinia biomass may allow the lower state to trap the system.