This paper uses the stochastic approach to convergence to investigate whether real per capita GDP in Portugal has been converging to the EU15 average. The estimation accounts for conditional convergence, transitional dynamics and up to two structural breaks. It is found that per capita GDP in Portugal has indeed converged to the EU15 average, but the pace of convergence has not been uniform along time. In particular, a slow down in the convergence process is identified in 1974. This result depends, however, as to whether the choice of this break-date is viewed as uncorrelated with the data. No evidence of acceleration in the speed of convergence is found after EC accession, in 1986.