The article is dedicated to the important scientific problem – the interpretation of the concepts of international and world order. Particular attention is paid to the conceptual approaches in the studying of the concepts of world and international order and legitimacy, as main condition for their formation. It is emphasized that international order is viable only if it is accepted voluntarily if not by all, but at least by the majority of international actors. It is studied that the concept of “world order” reflects the growing awareness of the common responsibility of people and nations for the state of our planet. Approaches to the world order formation and development in the XXI century are analyzed, the ideological sphere of the new world order, which is seen in globalization processes in the world, the concentration of world capital, the formation of special public opinion through the media. The authors consider the issue of a just and democratic world order, in this context, a special resolution of the UN General Assembly “Promoting Democracy and a Fair International Order” is mentioned. The article considers the concept of the famous American political scientist S. Hoffman, who proposes to distinguish between an international order that can exist without a world order and a world order that cannot be established without an international order. The types of international order are studied, in particular: competitive order, coordination order, subordination order, hegemonic order, imperial order, condominium order. The authors note the position of the American researcher and politician H. Kissinger, who argues that every world order is an expression of the desire for permanence, stability, foreign policy balance. However, all the elements that make it up are constantly changing, and this has the effect of reducing the duration of international systems. The article also considers the ideas of the collective world order of the American political scientist Z. Brzezinski. The authors highlight the views of the Club of Rome on the formation of international and world order.