  Superstatistics are superpositions of different statistics relevant for
driven nonequilibrium systems with spatiotemporal inhomogeneities of an
intensive variable (e.g., the inverse temperature). They contain Tsallis
statistics as a special case. We develop here a technique that allows us to
analyze the large energy asymptotics of the stationary distributions of general
superstatistics. A saddle-point approximation is developed which relates this
problem to a variational principle. Several examples are worked out in detail.
