  The Multivariate Extreme Value distributions have shown their usefulness in
environmental studies, financial and insurance mathematics. The Logistic or
Gumbel-Hougaard distribution is one of the oldest multivariate extreme value
models and it has been extended to asymmetric models. In this paper we
introduce generalized logistic multivariate distributions. Our tools are
mixtures of copulas and stable mixing variables, extending approaches in Tawn
(1990), Joe and Hu (1996) and Foug\`eres et al. (2009). The parametric family
of multivariate extreme value distributions considered presents a flexible
dependence structure and we compute for it the multivariate tail dependence
coefficients considered in Li (2009).
