  As is the case for the theory of holomorphic functions in the complex plane,
the Cauchy Integral Formula has proven to be a corner stone of Clifford
analysis, the monogenic function theory in higher dimensional euclidean space.
In recent years, several new branches of Clifford analysis have emerged.
Similarly as hermitian Clifford analysis in euclidean space R^{2n} of even
dimension emerged as a refinement of euclidean Clifford analysis by introducing
a complex structure on R^{2n}, quaternionic Clifford analysis arose as a
further refinement by introducing a so--called hypercomplex structure Q, i.e.\
three complex structures (I, J, K) which submit to the quaternionic
multiplication rules, on R^{4p}, the dimension now being a fourfold. Two,
respectively four, differential operators lead to first order systems invariant
under the action of the respective symmetry groups U(n) and Sp(p). Their
simultaneous null solutions are called hermitian monogenic and quaternionic
monogenic functions respectively. In this contribution we further elaborate on
the Caychy Integral Formula for hermitian and quaternionic monogenic functions.
Moreover we establish Caychy integral formulae for osp(4|2)--monogenic
functions, the newest branch of Clifford analysis refining quaternionic
monogenicity by taking the underlying symplectic symmetry fully into account.
