In this paper we give a precise definition of long-run causality in a multivariate non-stationary, possibly cointegrated, framework. A variable is said to be causal for another in the long-run if knowledge of the past of the former improves long-run predictions of the latter. In a VAR framework, we show that long-run non-causality can be easily tested with a Wald statistics, conditionally on the cointegration rank. The methodology is used to study long-run causal links between US, German, and French long-term interest rates from January 1990 to June 1997.