Résumé : We adopt a time-varying cointegration test to discriminate among different empirical studies claiming to find a stable Euro Area money demand equation. A time invariant relation explaining real balances is rejected by data, even when accounting for housing, financial and labour markets. Conversely, an international portfolio allocation approach provides stabilization. In particular, international financial markets, rather than monetary policy, are the key determinant of the observed diverging path of money growth. In terms of policy, we provide empirical support for a New Two Pillars Strategy aimed to achieve financial stability through money and credit and price stability through interest rates.