The emergence of a global community is accompanied by a realization that greater cooperation is essential to its welfare. This is particularly true in the area of crime prevention and control. The increase in international, transnational, transboundary and national crime has contributed to a genuine growth in the body of international criminal law. The most effective way to combat such crimes is for states to accept an obligation to try international criminal law offenders before their own courts or surrender them for trial before the courts of another state or an international court. Until such time as an effective system of international criminal justice is established, the duty to prosecute or extradite will remain the foundation for international criminal law enforcement. This book examines in detail the variety of international instruments which impose a duty to prosecute or to extradite. It asks how far this duty goes and whether one aspect of this obligation supersedes the other, and whether it can now be regarded as an obligation imposed by general international law. In discussing these questions, the book provides a highly illuminating account of the basic postulates of international criminal law and their relationship to competing visions of the nature of the international legal order. There is an evident need for international law to settle some of these questions. The ICJ, for example, needs to address the question in the case brought before it by Libya against the U.S. and the United Kingdom. Moreover, it will be a question of some significance with respect to the International Criminal Tribunal for the former Yugoslavia. Lastly, the prospect of a permanent international criminal court presently before the United Nations, is, in part, dependent on the effectiveness of aut dedere aut judicare.