We consider two multivariate long-memory ARCH models, which extend the univariate long-memory ARCH models, we first consider a long-memory extension of the restricted constant conditional correlations (CCC) model introduced by Bollerslev (1990), and we propose a new unrestricted conditional covariance matrix model which models the conditional covariances as long-memory ARCH processes. We apply these two models to two daily returns on foreign exchanges (FX) rates series, the Pound-US dollar, and the Deutschmark-US dollar. The estimation results for both models show: (i) that the unrestricted model outperforms the restricted CCC model, and (ii) that all the elements of the conditional covariance matrix share the same degree of long-memory for the period April 1979 - January 1997. However, this result does not hold for the floating periods March 1973 - January 1997 and September 1971 - January 1997. This break in the long-term structure may be caused by the European Monetary System inception in March 1979.