This paper presents a multivariate analysis of a money demand system in Europe. The system comprises real broad money, real GDP, the inflation rate, a long-term and a short-term interest rate. Two stable cointegration vectors can be identified: a money demand function and a long-run Fisher equation. Inflation does not play a role in the specification of the European money demand function. Stability of money demand is generally seen as a precondition for monetary targeting. No suggestive evidence for structural instability is found for long-run money demand. This is of particular relevance for the monetary strategy of the ECB.