Abstract: In 2002–2018, the inequality between Russian regions in terms of real personal incomes per capita was decreasing, which indicates convergence. In this context, real incomes mean that they are comparable across regions, being adjusted for regional price levels. This paper reveals the “anatomy” of the convergence process, finding the role of every individual region in it. To do so, regional time series of real incomes per capita are tested for catching-up with the national income per capita. Unlike the widespread methodology of testing convergence with the use of time-series methods, nonlinear asymptotically decaying trends model the convergence processes in this paper. The results obtained suggest that 54.4% of the Russian regions exhibit convergence, and 20.3% of regions maintain a stable (on average) income gap. At the same time, there is a significant proportion of deterministically diverging regions, equaling 22.8%. Two regions only (2.5%) do not exhibit a regular behavior. © Pleiades Publishing, Ltd. 2023. ISSN 2079-9705, Regional Research of Russia, 2023, Vol. 13, Suppl. 1, pp. S1–S12. Pleiades Publishing, Ltd., 2023.