The high degree of economic integration has led to an increased degree of currency substitution in the EU countries, which could bring instability in national money demand functions while an EU-wide money demand function could be more stable. Currency substitution usually takes the form of cross border deposits (CBD), which are not included in the traditional monetary aggregates. Thus, extended monetary aggregates that include the relevant CBDs are defined in this study. In order to investigate the implications of currency substitution for the stability of the demand functions, the traditional and extended monetary aggregates for five EU countries are defined in addition to EU-wide monetary aggregates. The estimated EU-wide demand for extended money appears to be stable suggesting that there is scope for monetary policy at the European level. However, the stability of the area-wide aggregate has been impaired when the relevant CBDs are not included.