In this paper we examine the extent to which countries are converging in per capita productivity levels. We propose to use cluster analysis in order to allow for the endogenous selection of converging countries. We formally define convergence in a time series analytical context, derive the necessary and sufficient conditions for convergence, and introduce a cluster analytical procedure that distinguishes several convergence clubs by testing for these conditions using a multivariate test for stationarity. We find a large number of relatively small convergence clubs, which suggests that convergence might not be such a widespread phenomenon.