  Under a mild condition we give closed-form expressions for copulas of systems
that consist of maxima and of minima of subvectors of a given random vector $X$
with continuous marginals. Said expressions appear explicit in the copula of
$X$ and the mentioned condition is for example met when the law of $X$ admits a
strictly positive density with respect to Lebesgue measure. In the i.i.d. case
these "maxmin" copulae become universal and the conditions on their validity
can be dropped entirely. Our main motivation comes from applications to shock
models that arise in multivariate survival theory. Another application is to
order statistics copulas.
