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Using the Johansen test for cointegration, we examine to which extent inflation rates in the Euro area have converged after the introduction of a single currency. Since the assumption of non-stationary variables represents the pivotal point in cointegration analyses we pay special attention to the appropriate identification of non-stationary inflation rates by the application of six different unit root tests. We compare two periods, the first ranging from 1993 to 1998 and the second from 1993 to 2002 with monthly observations. The Johansen test only finds partial convergence for the former period and no convergence for the latter.