Mankind is facing new civilizational problems (management of global processes, environmental safety, health care, etc.). A significant role in their solution is given to international organizations, interstate legal systems. Analysis of actions to solve global problems raises before legal science questions about the real capabilities of international organizations, interstate legal systems, their ability to adequately respond to globalization challenges, the need to clarify their role in the new reality, as well as their nature, form, and significance. This is a new model of interaction between states within the international system, which could ensure not only their cooperation but also integration through a new institutional mechanism and system of legal acts. The study uses universal and European international legal acts (in particular, sources of law) and other documents that offer a description of their nature, form, significance, ability to adequately respond to the globalization challenges of today. The main in the research process were: globalization approach, logical methods, general theoretical, sociological, comparative law, and international legal methodology. An analysis of the provisions of international, foreign, and Ukrainian legal science, sources of law, and legal practice revealed that modern international organizations arose in connection with the need to ensure the functioning of sovereign states and their cooperation. After the Second World War, those were formed that are designed to ensure closer cooperation based on universal and regional cooperation (United Nations, Council of Europe, European Union). New world order and interstate legal systems are being formed, which structure it. Their forms of integration are emerging, such as the legal system of the European Union. These systems have successfully fulfilled their role in streamlining the regional (European) and universal space. Although new globalization challenges of socio-economic, security, information, health, and environment necessitated the formation of a new model of interstate legal systems, which would ensure not only cooperation but also integration, through the creation of a new institutional mechanism and an effective system of legal acts.