  In this paper we carry out analysis and geometry for a class of infinite
dimensional manifolds, namely, compound configuration spaces as a natural
generalization of the work \cite{AKR97}. More precisely a differential geometry
is constructed on the compound configuration space $\Omega_{X}$ over a
Riemannian manifold $X$. This geometry is obtained as a natural lifting of the
Riemannian structure on $X$. In particular, the intrinsic gradient, divergence,
and Laplace-Beltrami operator are constructed. Therefore the corresponding
Dirichlet forms on $L^{2}(\Omega_{X})$ can be defined. Each is shown to be
associated with a diffusion process on $\Omega_{X}$ (so called equilibrium
process) which is nothing but the diffusion process on the simple configuration
space $\Gamma_{X}$ together with corresponding marks. As another consequence of
our results we obtain a representation of the Lie-algebra of compactly
supported vector fields on $X$ on compound Poisson space. Finally
generalizations to the case when the compound Poisson measure is replaced by a
marked Poisson measure easily follow from this construction.
