The purpose of this paper is to improve our understanding of government solvency in OLG models with a given sequence of government expenditures. In our view, public debt is allowed if its level does not preclude the existence of a competitive equilibrium. We first consider the case where the government can implement whatever amounts of lump-sum taxes. Then we show that there is no restriction on the path of public debt, and that the government is not constrained by any intertemporal budget constraint. When there are some restrictions on lump-sum taxes, then an equilibrium exists providing that a restriction on the level of public debt is satisfied. We pay special attention to the following restriction: at any each date, the amount of public debt is less that the value of the GNP at that date and less than the discounted value of the GNP one period after. Supposing that our restriction holds along a competive equilibrium path, we have investigated whether or not the intertemporal budgetary equilibrium condition holds. When the limit of the discounted value of the GNP is nil indeed, then the intertemporal budgetary equilibrium condition holds. Moreover, a Ponzi game is impossible. When the superior limit of the discouted value of the debt is strictly positive our condition does not imply the intertemporal budgetary equilibrium condition. A Ponzi game is also possible.