It does this by noting why it is important to study this phenomena; identifying some new elements that may be present when social control crosses borders; and suggesting some hypotheses for empirical testing to guide future theory and research. The study of policing across national borders can add to knowledge in at least 10 ways. It can assist in understanding the origins of domestic forms of control, and resistance to proposed new forms may also be partly understood by knowledge of past cross-border policing. Also, a focus across borders calls attention to the systemic aspects of many forms of crime and social control; and awareness of cross-border influences can help in understanding the dynamic nature of crime and enforcement patterns. Developments beyond the borders of a country may affect the supply of victims and offenders and the demand and supply of illegal goods and services. The most frequent forms of cross- border social control activity are border policing; unilateral, cross-border interventions; border crossings as protective services; multilateral patrols or investigations; operational, supranational organizations; police liaison officials; non- operational multinational organizations; multinational private policing organizations; joint training and sharing; and direction, training, and resources offered by a dominant system to others. After identifying what is different about social control that crosses national borders, the author presents 11 hypotheses about the future of social control across national borders, based on recent developments in Europe and North America. 9 notes