The EU-accession of Estonia, Latvia, Lithuania, Poland, Slovakia, Slovenia, the Czech Republic and Hungary in 2004 is more and more probable. Bulgaria and Romania may possibly enter in 2007. In order to later join the EMU, these countries have to meet the Maastricht Criteria. This paper reviews the economic relevance of the convergence criteria and their application with choosing the current EMU-members. Thereby, the question is also dealt with: does it make sense to force the fulfilment of the criteria before the transition is completed. Furthermore, the prospect of the ten Central- and Eastern European countries meeting the criteria, is considered. It seems as if a big bang in view of the EMU-enlargement will not occur.