The aim of the present article is to present the convergence criteria contained in the Treaty of Maastricht and the degree to which it has been actually observed by the countries belonging to the Euro zone in the last two decades. Also, it tries to give an answer to the question concerning the rapid moves on the monetary market (with the indication to the EUR/USD ratio) in the context of the discussed problems of excessive debts incurred by the south European countries. In their analysis the authors pay special attention to Greece.