Background: Invasive alien species receive little attention in many tropical countries. Aims: We examine the Neotropical tree genus Cecropia in West Java and ask how eradication decisions should be judged given limited resources. Methods: The distribution was determined based on field searches. The history, impacts and perceptions of Cecropia were examined through official records, observations, interviews and published literature. Results : At least four Cecropia species were planted in the Bogor Botanic Gardens, West Java Province, Indonesia, during the twentieth century but only C. peltata appears to have naturalised extensively. Since 1943 Cecropia has spread over 1290 km2. Implied mean rates of spread range from 0.13 km year?1 to 0.68 km year?1, with the fastest rates occurring down-slope and along river valleys. It has reached Jakarta to the north and the Mount Gede-Pangrango National Park to the south. It occurs only in open and disturbed locations. Local farmers consider Cecropia only a minor nuisance. We review 15 other reports of Cecropia naturalised outside the Neotropics. Conclusions: Without control, Cecropia may eventually become common throughout Java. There is no evidence that any serious problem will, or will not result. We call for the development and implementation of low-cost and decisive assessment procedures for evaluating the control and management of naturalised organisms.