The adoption of a common central Bank has modified the strategic relationships between fiscal and monetary authorities and raised in a new context the issue of debt stabilization. To study this problem, Van Aarle et al (1997) have proposed a two-country model with a common central bank. In a sense they obtained a neutrality result: the adoption of a common central bank does not modify the evolution of debt if the authorities can commit. This note reexamines this neutrality result by departing from the previous authors on three points: i) externalities are introduced between countries to account for the elasticity of the world interest rate to macro-economic policies, ii) the model features n countries, some of them remaining outside the monetary Union, iii) analytical results are given (many results of Van Aarle et al (1997) were numeric). In this extended context the neutrality result collapses: i) the institutional change introduces an asymmetry between countries, ii) countries inside the monetary union improve their long run welfare, iii) but the outside countries can win or lose under the new institutional setting.