This analysis departs from discussions on inequalities and cross-border mobility in the discussions on globalization and cosmopolitanism. One position argues that the most important factor determining the position in the hierarchies of inequality nowadays is opportunities for cross-border interaction and mobility. Those who take the counter-position hold that patterns of inequality in general and career patterns in labour markets in particular still tend to be organized mainly nationally or locally and not globally. In contrast to these two positions, the argument here is that cross-border transactions need to be captured more clearly, going beyond the global-local binary in the debate. One may usefully start from the concept of transnationality, that is, the continuum of ties individuals, groups, or organizations entertain across the borders of nation-states, ranging from thin to dense. This study addresses the question whether transnational ties are strategies of migrants to improve their social position and those of significant others in the countries of origin or other countries of settlement, or whether transnational ties constitute a social mobility trap.