This paper examines the process of convergence in Latin America over the period 1970–1998. There has been relatively little work on income convergence among developing countries in general and in Latin America in particular, even though many studies have examined convergence both within and among developed countries. There is little support for the convergence hypothesis over the sample period as a whole – although the beta coefficient is positive, it is insignificant. Convergence is strong in the 1970s but by the 1990s it has disappeared. There is no evidence of a narrowing in the cross-country dispersion of income (sigma convergence) for the sample period as a whole. The results offer little support for the neo-classical growth model – poorer countries have not grown faster than richer ones. There is a strong case for strengthening regional development policy.