In this paper we especially reconsider the convergence possibilities of long-term interest rates in the EMU member countries. The empirical evidence suggests that relevant convergence criteria in the Treaty and new information-generating and processing techologies have increased the transparency of main financial markets in Europe and so relatively quickly reduced the market segmenting effects of asymmetric information. In consequence, the range of financial transactions between member countries has remarkablely broadened. In the second stage of EMU, EU member countries have realized a general decline in nominal interest rates and interest rate differencials with Germany. However, this performance does not necessarily mean that economic structures of member countries became homogeneous and fiscal policy stances identical. For example, credit risk premia from the long-term interest rates prevailing on EU members debt are still differenciated, as reflecting the credit rating on national public debt set by Standard and Poor's and Moody's. These statistically significant credit risk premia would become even more important after the introduction of the Euro in the third stage of EMU, because exchange rate risk is completely abolished. Considering now the debt ratio to GDP and the present situation of harmonization process of EU tax systems more deeply, we find the following analitical results. First, even in the process of establishing monetary discipline and pursuing stability of price by ECB, there would not emerge the one euro yield curve in the EMU financial markets, because of the possible differences of credit risk on member governments' bonds as well as of fiscal policy stances. The same conclusion can be also confirmed by imcomplete convergence of term-structures of interest rates statistically. The adoption of a single currency, the Euro, would expedite, as generally accepted, the tax harmonization process, because monetary integration inevitablely deepens financial market integration and transparency. But such market-based tax harmonization is limited mainly in the areas of the value-added tax and other sales tax that are exposed to international competition. On the other side, tax harmonization for the income, profits, and capital gains tax and moreover for social security contributions is rather difficult to realize so promtly, because these tax areas are historically connected with social structures of each member countries. Second, a single monetary policy and tax harmonization would emerge eventually the difference of financial autonomy between member countries under the constraint of so-called stability pact. The EMU has two actors: one is the ECB that will set the common monetary policies. Another one is not single, but eleven member governments that will maintain a considerable degree of fiscal autonomy. Coordinating these two actors may be not simple and easy, especially in the case which any external shock falls very unequally on a few high-debted member coutries. High-debt countries would have incentive to decrease their debt ratio to GDP by pursuing prudent fiscal policies, solong the marginal benefit from decreasing debt ratio to GDP is larger than the marginal benefit from a common decrease in the interest rate controlled by ECB.