  Let $(G(X_j))_{j\geq1}$ be a multivariate subordinated Gaussian process,
which exhibits long-range dependence. We study the asymptotic behaviour of the
corresponding sequential empirical process under two different types of
subordination. The limiting process is either a product of a deterministic
function and a Hermite process as in the one-dimensional case or a sum of
various processes of this kind.
