Our analysis, based on a variety of standard econometric techniques, aims to be a fairly comprehensive test of the hypotheses about long cycles, associated with the name of Kondratiev/Kondratieff. Our work tries to link the issue of long cycles with the issue of economic convergence and divergence in the world system, because there are very strong cyclical ups and downs of relative convergence in the world system, observable not just in the “national” growth rates and “national” economic cycles. Already the Japanese economist Kaname Akamatsu, who lived from August 7, 1896 to December 20, 1974, and who was a great admirer of Kondratiev/Kondratieff, hinted at this connection. His most well-known tribute to Kondratiev/Kondratieff (Akamatsu, 1961) specifically links the rise and decline of the global peripheries to the larger Kondratiev/Kondratieff cycle. His contribution, which is hardly ever mentioned nowadays in the framework of K-cycle research, is the starting point of our analysis. In fact, these “Akamatsu cycles”, analyzed in this work, are even stronger and seem to be more devastating than the “national Kondratiev/Kondratieff waves” and world systemic waves themselves, leading to the discovery of what might be even termed a “double-Tsunami wave structure”. Both our re-analysis of world industrial production growth data since 1741 as well as the global conflict data since 1495, presented in this article, cautiously support the earlier contentions of world system research with evidence, tested by spectral analysis and auto-correlation analysis. Using the well-known and now updated Maddison data base at http://www.ggdc.net/maddison/maddison-project/data.htm, Kondratiev/Kondratieff cycles of around 60 years duration at a nation state level are most clearly visible in Argentina, Canada, and Russia, with evidence on the existence of longer cycles of more than 35 years also in Belgium; Chile; Greece; Netherlands; India; New Zealand; Spain; and USA; while for the other countries of the Maddison data set, earlier negative spectral density analysis results reported in the ample literature surveyed in this article could not be falsified. By contrast, the evidence about strong long term cycles of convergence seems to be very convincing. Future research is recommended to realize that convergence processes in most nations of the world are discontinuous and of a cyclical nature, thus supporting the pessimism inherent in the writings by the world systems scholar Giovanni Arrighi on the subject.