European Monetary Union will come into existence in 1999. This raises questions related to the monetary policy targets that will be adopted by the European Central Bank (ECB). For both likely candidates, targeting a money aggregate or an inflation target, the existence of a stable money demand function at a European level is important. In this paper estimates of such a European money demand for narrow and broad money for the actual 11 EMU countries based on quarterly aggregate data from 1964 to 1994 are presented. It is argued that statistically satisfactory and economically interpretable functions can be found. Moreover, the estimated models appear to be stable over a period of 20 quarters. This raises the hopes that the ECB will face a stable money demand and be able--at least for a certain time--to use past aggregate data for policy purposes. Copyright 1999 by Scottish Economic Society.