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This paper studies the convergence in the European Union on Purchasing Power Parity. Firstly, we develop a method for the estimation of PPP series and then, we put it into practice and estimate the monthly Purchasing Power Parity for the period January 1995 to July 2003. Secondly, convergence is studied using distribution dynamics from the continuous and discrete approximations. Results show some slow convergence in the European Union. Keywords: Purchasing Power Parity, Convergence, Distribution Dynamics, Markov Chains