The current discussion about stability of the European money demand function is flawed by a confusion of two different concepts of stability (adjustment speed versus error variance). The meaning and importance of the underlying notions of stability is clarified. It is demonstrated that necessary and sufficient conditions for the two types of stability are mutually independent and empirical issues. The issues are related to a distinction between a currency substitution effect and a portfolio diversification effect. The difference can also be related to the choice between discretionary and rule-oriented monetary policies.