  We consider the existence of bibundles, in other words locally trivial
principal $G$ spaces with commuting left and right $G$ actions. We show that
their existence is closely related to the structure of the group $\Out(G)$ of
outer automorphisms of $G$. We also develop a classifying theory for bibundles.
The theory is developed in full generality for $(H, G)$ bibundles for a
crossed-module $(H, G)$ and we show with examples the close links with loop
group bundles.
