Literature on convergence among Latin American countries is still scarce compared to other regions. Almost none of the research connects convergence to the economic history of Latin America and the usual finding is one speed of convergence assuming one globally stable steady-state. In this paper I analyze 32 countries and 108 years, more observations than any other study, which allows me to use chronological events to explain, analyze and validate the historical convergence clubs in Latin America, assuming multiple steady-states. The chronological time-line is divided into three important known phases, from which I find two to three convergence clubs. Following Thorp (1998), the first phase, called the exporting phase goes from 1900 to 1930, the second, the industrialization phase from 1931 to 1974, and the last one, the globalization phase from 1975 to 2007. During the last two phases, I find strong evidence of convergence among those clubs that succeeded in industrializing and / or building good institutions. The reason may be that technology diffusion and capital accumulation is easier when these two phenomena occur. Furthermore, I find no evidence that geographical aspects nor integration processes helped countries to converge.