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The aim of the article is to try to answer the question about the effects of accession of Poland to the European Union from the point of view of regional inequalities and convergence. The authors present a neoclassical model of exogenous growth with the balance of European Union's resources allocated to the cohesion and convergence policy implementation. The model is a generalization of the standard growth model of Solow and Swan. In the paper they describe the calibration methods for both types of growth models and the methods of establishing the values of the model variables in the steady state. They perform a retrospective analysis of regional inequalities in Poland for the period 2004-2006 and a prospective analysis based on the models of growth of the Polish economy and the regional economies of voivodships. They are interested in beta - conditional convergence, which is identified with the convergence of the growth paths of physical capital per employed worker and GDP per employed worker to stable steady states in neoclassical growth models with the balance of resources of the European Union and in standard Solow-Swan growth models for Poland and Polish voivodeships, which correspond to regions in the NACE2 nomenclature. The authors draw conclusions about the first effects of the cohesion and convergence program in Poland and the postulates for the principles of construction of new regional growth models as the instruments of description and analysis of convergence and regional inequalities.