The article considers methodological problems arising in the study and in forecasting international political developments which have to do with the synthesis of the world system, civilizational and other approaches. Trends in the development of the world system include interaction of the progressive and of the cyclic dynamics, which must be taken into consideration when forecasting global, regional and national transformations. Political cycles in the USA, Russian reforms-counterreforms, European integration trends demonstrate that political development progresses by way of cycles and waves as a means of selecting and affirming new institutions and mechanisms. The problem of convergence and collision of alternative forms of contemporary capitalism is analyzed.