  U-statistics of spatial point processes given by a density with respect to a
Poisson process are investigated. In the first half of the paper general
relations are derived for the moments of the functionals using kernels from the
Wiener-Ito chaos expansion. In the second half we obtain more explicit results
for a system of U-statistics of some parametric models in stochastic geometry.
In the logaritmic form functionals are connected to Gibbs models. There is an
inequality between moments of Poisson and non-Poisson functionals in this case,
and we have a version of the central limit theorem in the Poisson case.
