Using di¤erent unit root statistics and the approach of Tomljanovich and Vogelsang (2002), we test for the existence of stochastic and beta-convergence in the unemployment rates of a set of thirteen European countries. Using quarterly data for the period 1984:1-2005:4, we observe that there has taken place a convergence process in the majority of European unemployment rates. This process has become more intense since 1993.