The paper presents and analyzes the views of F. A. von Hayek on the issue of mutually competing private currencies and the possibility of abolishing the state monopoly on the issuance of money. The economists discuss whether the dollar or the euro has a less or greater chance of survival in a situation of financial and economic turbulence. BRICS countries, such as Brazil, Russia, India, China and South Africa, are questioning the future of the dollar as the main global currency. There are also proposals to create a single global currency. The IMF proposes the creation of a global bank to manage a single world currency. Contrary to these views, F. A. Hayek, the Nobel Prize winner for Economics, created the concept of so-called private money. Hayek’s conception is based on the statement that money supply can be better ensured by private issuers. Hayek believes that the existence of the generally accepted government monopoly on issuing money is not needed at all and even that it does not bring any benefits. He assumes that it would be possible to establish the institutions - banks of issue in various parts of the world, which would be entitled to issue mutually competing money. Money issued by various banks would have different denominations, and their relative value to other currencies could move freely. The bank of issue is interested to maintain a stable price level in terms of its currency relative to a certain basket of commodities. Hayek assumes that from several currencies that would be issued by private banks people always choose a better currency than the state currently provides. Hayek was against the creation of the single currency within the EU. He considered that the single currency would not be better than the individual national currencies. He suggested using the individual national currencies freely without restrictions and releasing banking business in all EU Member States. The existing monetary and financial institutions could achieve such discipline and responsibility that would ensure to issue reliable and stable money. Each country would issue only the amount of money that would ensure its stability. The governments could therefore not abuse the currency issuance to cover deficits and to solve other problems.