  For a given stationary max-stable random field $X(t),t\in Z^d$ the
corresponding generalised Pickands constant coincides with the classical
extremal index $\theta$ which always exists. In this contribution we discuss
necessary and sufficient conditions for $\theta$ to be 0, positive or equal to
1 and also show that $\theta$ is equal to the so-called block extremal index.
Further, we consider some general functional indices of $X$ and prove that for
a large class of functionals they coincide with $\theta$. Our study of
max-stable and stationary random fields is important since the formulas are
valid with obvious modifications for the candidate extremal index of
multivariate regularly varying random fields.
