  We determine the orbit types of the action of the group of local gauge
transformations on the space of connections in a principal bundle with
structure group O(n), SO(n) or $Sp(n)$ over a closed, simply connected manifold
of dimension 4. Complemented with earlier results on U(n) and SU(n) this
completes the classification of the orbit types for all classical compact gauge
groups over such space-time manifolds. On the way we derive the classification
of principal bundles with structure group SO(n) over these manifolds and the
Howe subgroups of SO(n).
