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This paper analyses the evolution of regional inequality in Brazil in the period 1939–1995. Based on a data set organized by the author, indicators of per capita income dispersion among states and regions are presented and their evolution over time is analyzed. The correlation between the regional initial level of per capita income and its growth is considered, testing for Beta convergence. The speed of convergence is calculated in two different forms, the neoclassical model and the coefficient of variation, the later allowing for the analysis of oscillations in inequality over time and its relationship to national economic growth rates. The Kuznetz hypothesis, relating regional income inequality and level of development, is tested. The results indicate the presence of signs of regional income convergence in Brazil, but with important oscillations in the evolution of inequality over time as well as across regions within …