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Demographers have yet to develop a suitable integrated model of international migration and consequently have been very poor at forecasting immigration. This paper outlines the basic elements of an integrated model and surveys recent history to suggest the key challenges to model construction. A comprehensive theory must explain the structural forces that create a supply of people prone to migrate internationally, the structural origins of labour demand in receiving countries, the motivations of those who respond to these forces by choosing to migrate internationally, the growth and structure of transnational networks that arise to support international movement, the behaviour states in response to immigrant flows, and the influence of state actions on the behaviour of migrants. Recent history suggests that a good model needs to respect the salience of markets, recognize the circularity of migrant flows, appreciate the power of feedback effects, and be alert unanticipated consequences of policy actions. [ABSTRACT FROM AUTHOR]