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In the context of EU enlargement there is no universal model which should offer a unique solution for diminishing the disparities in the development of a country. An approach only from the point of view of economic growth is not enough, so we extend the analysis towards the social development. Considering the level of GDP per capita and of HDI registered by EU states during 1995-2012, we test the hypothesis of real σ and β-convergence in terms of economic and social development. The estimated results indicate a tendency in reducing the divergence in both economic and social degree of development. A relatively strong process of real σ-convergence became evident while real β-convergence testing supports the hypothesis among EU countries, but the results indicate a slower process for HDI convergence compared with GDP per capita. [ABSTRACT FROM AUTHOR]