Studies about convergence in Brazil have concentrated in the ß and (-convergence analysis. In this thesis is presented a new methodolgy to study convergence, that analyses how the income distribution among brazilian states and municipalities evolves over the time. Three kinds of estimation are done: a) kernel smoothed densities are estimated to allow the visualization of the changes occurred over the time in the distributon as a whole, while ß and (-convergence estimate only one parameter of this distribution; b) estimation of stochastic kernels to analyse the movements of the economies over the income space with the aim to identify convergence clubs in specific space intervals; c) estimation of stochastic kernels conditional on geographic localization, education, openness to international trade and income inequality, with the objective to identify possible explanations to the observed pattern of convergence. The use of the methodologies above allowed to identify that, although there is a convergence trend among brazilian municipalities in the period from 1970 to 2000, coexists with this trend a divergent movement that is leading to the formation of two convergence clubs among brazilian municipalities. Geographic localization and initial level of education appeared as important conditioners of the observed growth.