  We study a generalization of higher gauge theory which makes use of
generalized geometry and seems to be closely related to double field theory.
The local kinematical data of this theory is captured by morphisms of graded
manifolds between the canonical exact Courant Lie 2-algebroid $TM\oplus T^*M$
over some manifold $M$ and a semistrict gauge Lie 2-algebra. We discuss
generalized curvatures and their infinitesimal gauge transformations. Finite
gauge transformation as well as global kinematical data are then obtained from
principal 2-bundles over 2-spaces. As dynamical principle, we consider first
the canonical Chern-Simons action for such a gauge theory. We then show that a
previously proposed 3-Lie algebra model for the six-dimensional (2,0) theory is
very naturally interpreted as a generalized higher gauge theory.
