Using the stochastic kernel, we analyse the Hungarian convergence path before and after accession to the European Union (EU), within its NUTS 3 regions (counties), and between those of the eastern EU Member States. Then, we develop a convergence analysis of GDP per capita PPS (Purchasing Power Parity) conditioned to Common Agricultural Policy (CAP) funds, in order to understand the role of the introduction of the CAP in the convergence of Hungarian rural areas. We find increasing divergence both within Hungarian NUTS 3 regions and between the eastern EU MS NUTS 3 regions, especially after Hungary joined the EU; a limited contribution of the CAP to the catching up of rural areas; and persisting difficulties of working with lacking rural disaggregated statistics.