This paper extends the FIGARCH long-memory volatility model to a multivariate framework. The proposed quasi maximum likelihood estimator for the parameters of the model is analyzed through Monte Carlo simulations and is found to perform satisfactorily. A trivariate specification is applied for modelling jointly the daily volatility of foreign exchange rates of the German mark, British pound and Japanese yen against the U.S. dollar. The empirical example shows the relevance of the model and its suitability for practical risk applications.