The author argues that the emergence of the first permanent intergovernmental (IIGO) and non-governmental (INGO) organizationsin the second half of the XIX-th century was due to common causes. He tries to justify the need to consider them not as independent objects of study, but as the phenomenon, caused by the high level of internationalization of economic life of states and of socio-economic consequences of the industrial revolution, reached in this period. The emergence of IIGOs, based on international treaty, was accompanied by establishment of a large number of INGOs operating in similar fields of human activity, which performed supplementary functions and regulated areas of cooperation and public needs, not covered by interstate agreements. The article presents the main factors that in later stages of internationalization and development of contemporary international relations gave the impetus to emergence and development of international organizations, including the military-technological revolution, that gave birth to mass destruction weapons and avalanche-like growth of the number of human and material losses during wars and military conflicts, the Cold War between world communism and world capitalism, the collapse of the colonial system and formation ofa new main contradiction of the world politics between the "Club of rich countries" and states of the "global periphery", beginning of development of regional integration processes and, finally, the emergence of global problems. The article emphasizes that both IIGOs and INGOs evolved from the supportive tools in implementation of multilateral interaction of sovereign states towards becoming an integral part of contemporary international relations, fulfilling many vital functions of modern human society and its citizens. Given the involvement of the overwhelming majority of modern sovereign states and tens of thousands of civil society organizations in activity of numerical IIGOs and INGOs, none of the existing centers of world power can afford to trample down and to subordinate activities of all these international organizations. The development of IIGOs and INGOs makes any attempts to create a unipolar system of contemporary international relations impossible.