A stable and predictable demand for money function is a pre-requisite for the use of targets for monetary aggregates as a suitable intermediate objective of monetary policy. In spite of the clear difficulties which have manifested themselves in the estimation of such money functions, empirical interest has been renewed over the last decade driven by the belief that a stable long-run money demand relationship continues to exist. This revival of activity in this area was aided and abetted by the coming on stream of new econometric techniques, especially in the area of cointegration analysis and error correction models. Using these new econometric techniques, this paper looks again at the aggregate data for the Euro Zone countries and for the Community as a whole and tries to answer the question of whether a stable, cointegrating, money demand function exists at the Euro Zone and EC15 levels.