The problem of real convergence across economies has given rise to an in-tense debate among macroeconomists. The cross-section methodology, the most commonly-used in this field, has supported the convergence hypothesis, usually when conditioning to the steady state. Nevertheless, criticisms of this approach have helped the development and use of alternative methodologies. In this paper, we employ cointegration to analyze the GDP per capita time series of the EU member states, in order to examine the long-run relations-hips between them. Thereafter, and in an attempt to overcome the assumption of a unique trend for the whole series we introduce some models capable of dealing with the possibility of structural changes in a single series and detec-ting (endogenously) the exact moment of the break.

Keywords: catching up, cointegration, convergence, output per capita, unit roots.