Eradication of an invasive species is a holy grail sought by land managers, scientists and policy makers alike. This prize is particularly attractive to funding bodies that foresee a one-off investment to solve a problem. We evaluate a 20-year eradication project on the annual weed Martynia annua L. from remote Gregory (Jutburra) National Park in northern Australia. M. annua was regionally introduced in the 1860s and has since become naturalised and locally abundant on some pastoral properties. When land use changed from grazing to national park in the mid 1980s, M. annua was thought to be a serious problem. An eradication project was started in the late 1980s. Eradication of all individuals from within the National Park has not been successful but there have been other benefits of the project. We analysed operational, biological, social and economic criteria to find that the principal barriers to eradication were: occasional inaccessibility during the crucial seed production window; many widely dispersed small infestations; a perennial seed bank; and long-distance dispersal mechanisms. The two successes of the project were control of the weed to a level where ecological impact was negligible; and extensive community engagement. A novel approach adopted by the National Park, a biannual event called the Devil's Claw Festival, has trained and educated hundreds of local, national and international people about biological invasions and conservation issues in remote northern Australia. Long-term institutional leadership and investment have been crucial for this project. We offer recommendations to policy makers embarking on eradication projects of widespread rangeland weeds. � Australian Rangeland Society 2010.