In studies on regional and local development, the subject of interest are disproportions between territorial units constituting a given municipality. Changes in these categories over time are an important quality, too. This leads to the formulation of the concepts of convergence and divergence processes in the economic development of the studied units. The object of this paper is the analysis of the occurrence of real economic convergence at the level of municipalities using the example of Lubusz Voivodeship, in which study two measures relating to their income have been applied. The one is the municipality’s own income as a measure of economic activity in its area. The other one is personal income of the population as a measure of the level of its wealth. Using the Theil index and regression models, the occurrence of beta and sigma convergence phenomena in both income categories in municipalities were investigated. The analysis was conducted on the basis of data derived from the Local Data Bank of the Central Statistical Office, covering the 1999–2019 period. The results indicate that both the beta and sigma convergence phenomena do take place in the development of municipalities’ own income in the analyzed period. The above regularities, due to the volatility of tendencies, cannot be stated in the case of the personal income of the population.