We examine a balanced panel of globalization indices for 129 countries over the years 1991- 2010. We report evidence of cross-country sigma convergence in the overall globalization index. Sigma convergence also holds for each of the economic, political, and social globalization indices, as well as each sub-index within these indices. However, the evidence for stochastic convergence, based on panel unit root tests, is only strong for the political globalization index. Regarding the economic and social dimensions of globalization, respectively, we find evidence for stochastic convergence only in the flows and cultural proximity sub-indices. For the OECD subsample, evidence supports stochastic convergence for the overall, economic and political globalization indices. Evidence to support regional convergence among the non-OECD nations on various globalization dimensions is much more limited. Our findings indicate that globalization convergence is truly global only on the political dimension.