Since 2000, South American economies have undertaken several regional projects to eliminate socioeconomic inequalities and improve citizens' living standards. This study evaluates the convergence in real GDP per-capita, as a suitable proxy measure, of 10 Unasur members, namely Argentina, Bolivia, Brazil, Chile, Colombia, Ecuador, Peru, Uruguay, Paraguay, and Venezuela, for the period 1951-2011. By relying on cointegration techniques and applying Bernard and Durlauf's (1995) stochastic definitions of convergence and common trends, the presented evidence supports the existence of common long-run trends driving output in South America, meaning that the region is involved in a dynamic process of convergence in living standards.