This article investigates the occurrence of per capita income convergence in 19 Latin American countries. We apply a time series approach to test for stochastic convergence and β-convergence based on structural breaks unit root tests, where the dates of breaks are unknown and determined endogenously. This approach is essential since it does not impose common break dates and parameter homogeneity among countries. In fact, the econometric methodology employed attempts to provide what was lacking in previous works. As a consequence, unlike prior studies the results indicate that there is substantial evidence in favor of conditional convergence in Latin America. We show that this evidence is even greater when analyzing South and Central America separately.