Institutions of modern societies have often been argued to evolve, but their evolution is rarely examined in Darwinian and empirical terms. Here we use the categorical data set MaxRange on nations’ regime-types and their constituting institutions historically for analysis of their phylogeny. The MaxRange data set covers all nations in the world system of nations since 1600 with details on accountability structures, executive strength and degree of centralization, constitutional strength, democracy and other aspects of the political systems. We describe and analyze the character of the “true phylogeny” of regime-type evolution in the nations of the world 1600--2020. Our results indicate that evolutionary network rather evolutionary tree models have superior fit to data. Using the extracted phylogeny, we also investigate the dynamic networks of nations in terms of regime-types, accountability structures and their related background factors such as religions and language. Network centrality measures of nations and regime-types provide new important explanatory variables for network-adjusted survival analyses of various institutions, from types and levels of democracy to details of regime-types, including institutions like parliamentarism, presidentialism, and their hybrid forms.