During the last 15-20 years, inequality between Russian regions in terms of real personal incomes per capita was decreasing. This paper aims at revealing the "anatomy" of this phenomenon. To do so, time series of every regional income per capita is tested for catching-up with the national income per capita. Nonlinear asymptotically subsiding trends model the processes of convergence. The data cover 2002-2018 with a monthly frequency. Real incomes are estimated by adjusting nominal incomes to regional price levels. The results obtained suggest that 54.4% of the Russian regions exhibit convergence, and 20.3% of regions retain (approximately) stable income gap. At the same time, there is a significant proportion of deterministically diverging regions, equaling 22.8%. Random walks are detected in two regions only.