The cycles-and-waves approach is one of promising scientific instruments of explaining and predicting processes of political systems' development and modernization. The purpose of the presented round table as conceived by the journal was to review and, to a certain extent, to sum up the development of methodological aspects of the theme claimed, and to find out such spheres of the political where the application of the cycles-and-waves approach in the research could prove most efficacious. Participants of the discussion had been invited to have their say on three main questions: (1) To what extent are cycles (waves) models heuristic for the analysis of political systems' development? (2) Which of the known cycles-waves models are the most promising? (3) What are the benefits to derive from the cycles-and-waves approach so as to make for comprehension of political history and contemporary political development of Russia? Those participating in the discussion of these questions are: S.F.Chernyakhovsky, professor, Ecological-Political University; M.V.Ilyin, editor-in-chief, Polis journal; V.V.Lapkin, research worker, Institute of World Economy and International Relations, Russian Academy of Sciences; B.V.Mezhuyev, editor, Polis Electronic Information Centre; Ye.N.Moshchelkov, professor, Philosophical department, deputy pro-rector, Moscow State University; V.I.Pantin, senior research worker, Institute of World Economy and International Relations, Russian Academy of Sciences; G.Yu.Sitnyansky, senior research worker, Institute of Ethnography, Russian Academy of Sciences.