The Maastricht Treaty has acknowledged, and translated into precise criteria and indicators, the need for increased economic convergence to enter the final phase of Economic and Monetary Union (EMU). In this paper, we examine the improvement in the process of economic convergence since the creation of the EMS in 1979 and until mid-1992, as well as the expectations of market participants on the evolution of the process over the period 1992–96. We also try to assess the extent of the adjustment still to be made by comparing it to the adjustment already implemented during the 80s. We reach four main conclusions: (i) Economic convergence, expressed in terms of inflation, interest, and exchange rates, has improved considerably during the life of the EMS, but remains incomplete and differentiated amongst countries (ii) Market participants do not expect a significant improvement in the convergence process over the next five years (iii) The adjustment still to be made, which should basically affect the budget deficit and the rate of inflation, seems to be beyond the reach of Greece, extremely demanding, but not impossible, in the case of Italy, Spain and Portugal (iv) Successful adjustment policies and confidence of market participants on the results of such policies are thoroughly interlinked and cannot survive in isolation.