  We study the extreme value distribution of stochastic processes modeled by
superstatistics. Classical extreme value theory asserts that (under mild
asymptotic independence assumptions) only three possible limit distributions
are possible, namely: Gumbel, Fr\'echet and Weibull distribution. On the other
hand, superstatistics contains three important universality classes, namely
$\chi^2$-superstatistics, inverse $\chi^2$-superstatistics, and lognormal
superstatistics, all maximizing different effective entropy measures. We
investigate how the three classes of extreme value theory are related to the
three classes of superstatistics. We show that for any superstatistical process
whose local equilibrium distribution does not live on a finite support, the
Weibull distribution cannot occur. Under the above mild asymptotic independence
assumptions, we also show that $\chi^2$-superstatistics generally leads an
extreme value statistics described by a Fr\'echet distribution, whereas inverse
$\chi^2$-superstatistics, as well as lognormal superstatistics, lead to an
extreme value statistics associated with the Gumbel distribution.
