As soon as the ten new member countries have fulfilled the convergence criteria of Maastricht they can be accepted for accession to the European Monetary Union. By now, these countries pursue quite different monetary policies strategies in order to reach a high degree of monetary convergence, including different exchange rate systems. Since the new Eastern European countries are in a transformation process with partly difficult disinflation processes it is especially important to adopt the best strategy available. Therefore, information on the relative success of the different monetary policy strategies seems important, for if certain strategies can be identified as more successful than others, it makes sense for the other countries to adopt them. In that way the overall monetary convergence process in the new EU member countries could be improved. In what follows, the different monetary policies are theoretically described. This is followed by a description of the monetary policy strategies as they have been applied during the 1990s. In order to determine the relative success of these strategies the position of each country relative to the average of the ten new member countries is determined on the basis of five indicators: GDP growth, rate of inflation, current account balance, real effective exchange rate, and budget deficit. It turns out that the three Baltic States as well as Poland and the Czech Republic have so far been more successful than Slovenia, Slovakia and Hungary. Furthermore, a regime of either fixed or flexible exchange rate systems seems to be superior to any point on a continuum between this two "border points".