The place and importance of the fiscal criteria and the excessive deficit procedures (EDP) within the set of the Maastricht convergence criteria, as well as their basic importance for the Stability and Growth Pact (SGP) were presented. Also, the evolution of the attitude of the EU zone countries towards these criteria before and after the birth (1999) of the euro zone was shown. The extent was examined to which the Maastricht Treaty criteria and the SGP provisions were applied in the period of 1999–2003 by the EU organs when assessing the fiscal policy of individual countries under the excessive deficit procedure. Despite the fact that the admissible ceiling of the deficit-to-GDP ratio had repeatedly been considerably overstepped by the majority of the euro zone countries, no sanctions or penalties were ever applied. The EU organs confined themselves only to the so-called early warning to the countries concerned. The primary reason for the EU organs' abstention from applying the Treaty criteria and the SGP provisions was the fact that the Maastricht Treaty had adopted the nominal deficit as the basis for the assessment whether and to what extent the given country had infringed the fiscal discipline. Whereas, in a situation where the GDP is growing more slowly than the potential rate of growth, it is necessary, in order to avoid adverse consequences of a restrictive fiscal policy, to be guided by the structural rather than nominal deficit. Despite the infringement of the principle of avoiding an excessive deficit by the biggest euro zone countries and the lack, even in cases of drastic infringement of the fiscal discipline, of applying the sanctions and penalties foreseen by the Excessive Deficit Procedure, both the EDP and the Stability and Growth Pact have fulfilled their function of non-discretionary tools of public finance improvement both in the euro zone and throughout the EU, as the ED procedure applies to all the EU member countries. It was against this background that the Polish programme of fiscal convergence for 1995-1997, being a part of the general convergence programme filed in connection with the country's EU accession, was analyzed. The analysis has shown that, among the tasks under the above convergence programme, there are some that can prove to be very difficult to implement: 1- the adjustment of the Polish regulations (inclusive of the constitutional provisions) governing the position of the central bank to the requirements of the Maastricht Treaty, the ECB constitution and the statutes of the European System of Central Banks; 2- the need to accept after 2007, i.e. at the time when Poland's membership of the euro zone can become practical, that the Open Pension Funds (OPFs) do not make a part of the public sector and, consequently, the resources gathered by them are not public funds and, thereby, the liabilities of the Social Insurance Fund to the OPFs are public liabilities that augment the ratio of the public sector deficit and the public debt to the GDP.