Summary: A well-functioning international monetary system (IMS) should provide a satisfactory international liquidity and facilitate money and capital flows in the world economy. In a crisis, the IMS is expected to facilitate capital flows in order to eliminate imbalances leading to the crisis. The main leverage of the IMS in the postwar period was the dollar convertibility into gold, which enabled the US currency to become a global reserve currency. US monetary policy in this monetary system has a basic mission to generate international liquidity. When President Nixon suspended convertibility of the dollar to gold in 1971, this situation led to the collapse of the Bretton Woods system, the dollar began to float freely, but remained the key global reserve currency until today. The 2008 global financial crisis reminded us about the weakness of the current IMS, because the unstable value of the dollar created the risk of US dollar-denominated reserve assets. The current crisis has renewed the objections by the countries with the largest foreign exchange reserves in the world about "exorbitant privilege" of the U.S. dollar in the IMS, as Charles De Gaulle once called it. The monetary policy impulses in the countries whose currencies belong to the club of leading world currencies (primarily the US, Eurozone and Japan) are transferred outside the borders of these countries and affect other countries in the globalized world economy. This paper deals with the consequences of the present IMS structure, which is characterized by the dominant role of the dollar and the euro in international trade and financial flows. The paper studies the channels of US and Eurozone monetary spillovers into the international environment, and their consequences for other countries.