  In previous work the framework for a hypercomplex function theory in
superspace was established and amply investigated. In this paper a Cauchy
integral formula is obtained in this new framework by exploiting techniques
from orthogonal Clifford analysis. After introducing Clifford algebra valued
surface- and volume-elements first a purely fermionic Cauchy formula is proven.
Combining this formula with the already well-known bosonic Cauchy formula
yields the general case. Here the integration over the boundary of a
supermanifold is an integration over as well the even as the odd boundary (in a
formal way). Finally, some additional results such as a Cauchy-Pompeiu formula
and a representation formula for monogenic functions are proven.
