This paper investigates the per capita income convergence patterns of a set of Association of South East Asian Nations (ASEAN) and South Asian Association of Regional Cooperation (SAARC) countries. We obtained a time-series analysis for stochastic convergence by applying unit-root tests in the presence of two endogenously-determined structural breaks. We then supplemented the results by tests that produced evidence for b convergence. The evidence shows that the relative per capita income series of ASEAN-5 countries were consistent with stochastic convergence and b convergence, but this was not found for SAARC-5 countries. For the ASEAN-5 countries, the structural breaks associated with the world oil crisis and the Asian crisis impacted heavily on the convergence/divergence process.