The article investigates a problem of the euro introduction by new members of the European Union. It presents some potential benefits and costs of entry to European Monetary Union in the context of its present and future functioning. Then it discusses some advantages and disadvantages of postponing joining the euro-zone. Besides, potential meaning and consequences of giving a target date of introduction of the euro by a country and possible scenarios that can be taken at this way are presented in the paper. Since the 1st January 2007 Euroland comprises 13 countries. The finance ministers of EU member states have approved of Slovenia's admission to the euro area. The application of Lithuania was rejected - European Commission and European Central Bank have judged that it has not fulfilled the inflation convergence criterion. With regard to this event, the article touches an issue of the need for reconsidering the Maastricht criteria which presently seem to be a source of many content-related and interpretation doubts. It also investigates the requirement for adjusting the convergence criteria to the fact that the euro-zone has already been in existence.