Monetary growth in the euro area has exceeded its target level especially since 2001. Likewise, recent empirical studies did not find evidence in favour of a stable long run relationship between the variables entering the money demand function. Instead the equation appears to be increasingly unstable if more recent data are included. Since the link between money balances and macroeconomic variables seems to has become rather fragile, these results put serious doubts concerning the rationale of monetary aggregates in the monetary policy strategy of the ECB. However, if the analysis is done without imposing a short run homogeneity restriction between money and prices, a stable long run money demand relationship can be identified, where recursively estimated parameters are almost stable. In addition, the corresponding error correction model survives a wide array of specification tests, including procedures for nonlinearities and parameter instability. Hence, the apparent monetary overhang is in line with standard models of money demand behaviour, and is not expected to lead to a rise in inflation.