On the grounds that the global financial crisis during recent years has resulted in a significant increment of the government debt, in many OECD countries, especially in the "south-block", government debt stabilization has taken a central stage in issues to be addressed. In this paper we focus on the fact that financial markets are adding pressures on countries that appear vulnerable when looking at the current levels of debt, as well as the current rate of change of the debt. This takes the

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... m of requiring risk premia. The term we introduce, that depends on the rate of change of debt, represents apart from another form of pressure added by financial markets, can also be used to represent a measure of reward given by markets to governments that succeed in decreasing their debts. This term associated with the derivative of the governmental debt adds a strong nonlinearity to our mathematical model. In addition, when considering the Euro Area, an additional singularity arises: the members of the union are have a common monetary policy which is applied centrally by the E.C.B, in contrast with fiscal policy which is applied by each member country per se. This is also the case in most industrial countries, the size of fiscal deficits and the growth of monetary base are selected by two independent authorities. This suggests that we are facing a Two-Player Nonlinear Dynamic Nash Game under two modes of play, where the two authorities do or do not cooperate. Thus we analyze and solve under the Open-Loop Non-Cooperative mode of play and then under the Cooperative mode of play. We also investigate the finite time horizon, in addition to the infinite one, taking therefore a more practical approach as being bound in a policy for practically a really long time is sometimes of no application.