The objective of this article is to investigate cross-border real economic convergence, defined as the process of reducing the asymmetry of the economic development of cross-border areas in the conditions of European (territorial) integration. The analysis applies the relative asymmetry index which compares the level of regional gross domestic product (GDP) per capita (purchasing power standards - PPS) of neighbouring border areas. Its results confirm the occurrence of σ-convergence (in the periods 1980-85, 1985-94 and 2004-15) and absolute cross-border β-convergence (in different subperiods in the period 1980-2015). The obtained results also suggest that cross-border convergence generally progresses slower than convergence at the international level.