On January 1,1999 euro became the currency for 11 member states of the European Union. Since then the dollar-euro exchange rate has completed a full turning. Three years of depreciation of the euro followed by three years of appreciation without wild fluctuations asks for an explanation which would adequately account for the position of the euro as an emerging international currency. In this paper, first we present a concise summary of the theory of world money. Then we apply the theory to explain the development of the exchange rat of euro versus dollar in the subperiods 1999-2002 and 2002-2004.