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.
