Introduced animals, particularly mammals, continue to extinguish indigenous species in many parts of the world. This effect is greatest on oceanic islands but continental biotas are also affected. Case histories are used to illustrate difficulties of separating alien animal effects from other extinction agents, and of predicting outcomes. Further research is needed on synergistic and flow-on effects that may follow establishment of a new alien species. Combatting the introduction problem is seen as primarily one of attitude rather than of scientific understanding. It is recommended that in each country: risk analyses are made to identify problem species likely to be introduced; preventive measures are maintained against invasions by these aliens; contingency plans are established for rapid responses to invasions; intensively managed refuge areas are created to protect vulnerable indigenous species from alien species already present; further research is coupled with these actions; information on the introduction problem is disseminated more widely within countries; and international sharing of information on preventive and control measures is promoted more vigorously.