We assess monetary convergence preceding the implementation of the European Monetary Union (EMU) through Kalman filtering estimates of the risk premium of eleven forward exchange rates of European and non-European currencies. Since all participating currencies are in effect identical from inception of a currency union, the convergence process to such an identical status should be reflected in the participating currencies' risk premiums prior to monetary union implementation. Starting from this assumption, we show the paths followed by the participating currencies towards monetary union. We find that the co-movements of risk premiums among the preceding European Monetary System (EMS) currencies differ across time periods but display a tendency to convergence to the German mark’s risk premium up to EMU implementation. The paper also shows a clear pattern of asymmetry of the participating currencies in relation to the German mark.