  We give necessary and sufficient conditions for two sub-vectors of a random
vector with a multivariate extreme value distribution, corresponding to the
limit distribution of the maximum of a multidimensional stationary sequence
with extremal index, to be independent or totally dependent. Those conditions
involve first relations between the multivariate extremal indexes of the
sequences and secondly a coefficient that measure the strength of dependence
between both sub-vectors. The main results are illustrated with an
auto-regressive sequence and a 3-dependent sequence.
