Some recent studies suggest the possibility of estimating a stable aggregate demand-for-money relationship for the group of countries participating in the European Monetary System. These results are of particular relevance in connection with the task of setting policy targets for a European Central Bank. This paper uses a theoretical error-invariables framework to identify what is gained and what may be lost through cross-border aggregation of money demand. It provides an analytical basis for such studies, paying particular attention to currency substitution and international portfolio diversification.