  The category of exploded torus fibrations is an extension of the category of
smooth manifolds in which some adiabatic limits look smooth. (For example, the
limits considered in tropical geometry appear smooth, also degenerations
corresponding to an algebraic family with normal crossing singularities are
smooth.) In this paper we prove a compactness theorem for (pseudo)-holomorphic
curves in exploded torus fibrations. In the case of smooth manifolds, this is
just a version of Gromov's compactness theorem in a topology strong enough for
gluing analysis.
