  In the first part of this paper we consider a general stationary subcritical
cluster model in $\mathbb{R}^d$. The associated pair-connectedness function can
be defined in terms of two-point Palm probabilities of the underlying point
process. Using Palm calculus and Fourier theory we solve the Ornstein-Zernike
equation (OZE) under quite general distributional assumptions. In the second
part of the paper we discuss the analytic and combinatorial properties of the
OZE-solution in the special case of a Poisson driven random connection model.
