The concept of the power legitimacy as one of the problems in the field of public administration was first mentioned by the German jurist G. Jellinek of the late 19th - early 20th century, then it was deeply developed in the theory of political domination by M. Weber. Realizing the importance of this issue, scientists from different countries one way or another turned to it and refined its various aspects. This article provides a critical analysis of the basic concepts of the legitimacy of power, based on the contribution to the development of this issue by M. Weber, D. Easton, I. Cerovac, J. Rawls, D. Estlund and J. Habermas. Since the problem of the legitimacy of power is directly related to the maintenance of a democratic regime, the declared concepts are considered in the context of the varieties of democracies for which they were created. The purpose of this study is not only to analyze successive concepts of the legitimacy of political power, but also to identify their relationship with the prevailing ideas about democracy in science and society at the time the concept appeared. The study was carried out within the framework of a systematic approach using general theoretical methods of analysis and synthesis, systematization and classification, as well as the case study method for country analysis.