  We introduce the concept of Spin^G-structure in a SO-bundle, where $G\subset
U(V)$ is a compact Lie group containing $-id_V$. We study and classify
$Spin^G(4)$-structures on 4-manifolds, we introduce the G-Monopole equations
associated with a $Spin^G$-structure. On Kaehler surfaces a Kobayashi-Hitchin
correspondence can be proved for the corresponding moduli spaces. Using this
complex geometric interpretation, we determine explicitely a moduli space of
"PU(2)-Monopoles" on $\P^2$, we describe its Uhlenbeck compactification, as
well as the Donaldson- and the abelian locus.
