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We study the convergence properties of inflation rates among the countries of the European Monetary Union over the period 1980–2013. Recently developed panel unit root/stationarity tests cannot reject the stationarity hypothesis. This implies that some countries have been in the process of converging absolutely or relatively. By using a clustering algorithm we statistically detect three absolute convergence clubs in the pre-euro period, which comprise early accession countries. In particular, Luxembourg clusters with Austria and Belgium, while a second sub-group includes Germany and France and the third The Netherlands and Finland. We also detect two separate clusters of early accession countries in the post-1997 period: a sub-group with Germany, Austria, Belgium and Luxembourg, and one with France and Finland. For the rest of the countries/cases we find evidence of divergent behavior. Robustness is checked by testing pairwise convergence in a Bayesian framework. The outcome broadly confirms our findings.