Is there a stable aggregate money demand relationship for Europe? If so, why, and if not, why not? These questions are important for the implementation of policy by a European central bank, as well as for the appropriate speed of transition to EMU. This paper addresses them in a multi-country empirical study of money demand for the G-7 countries during the period since 1973. It looks for evidence of currency substitution and tests the restrictions implied by cross-border aggregation within Europe.