  The action of Ashtekar's generalized gauge group $\Gb$ on the space $\Ab$ of
generalized connections is investigated for compact structure groups $\LG$.
  First a stratum is defined to be the set of all connections of one and the
same gauge orbit type, i.e. the conjugacy class of the centralizer of the
holonomy group. Then a slice theorem is proven on $\Ab$. This yields the
openness of the strata. Afterwards, a denseness theorem is proven for the
strata. Hence, $\Ab$ is topologically regularly stratified by $\Gb$. These
results coincide with those of Kondracki and Rogulski for Sobolev connections.
As a by-product, we prove that the set of all gauge orbit types equals the set
of all (conjugacy classes of) Howe subgroups of $\LG$. Finally, we show that
the set of all gauge orbits with maximal type has the full induced Haar measure
1.
