Previous studies on economic convergence have been handicapped by the lack of sufficient serial data. Real GDP per capita are now available for 56 states. With some interpolation, we create series from 1870 to 1992 for Northern (developed countries) and Southern (lesser developed countries) aggregates. The data are explored by extending the leadership-long cycle perspective to deal with convergence. We find that North–South inequalities, at least those based on GDP per capita data, have been expanding. The corresponding growth rates reveal long waves, providing an important clue related to iterations of radical technological changes and their incomplete diffusion in explaining the North–South gap. We believe that convergence is unlikely any time soon without radical restructuring of global economic growth prospects.