  We use ensembles of high-resolution CDM simulations to investigate the shape
and amplitude of the two point correlation function of rich clusters. The
standard scale-invariant CDM model with $\Omega=1$ provides a poor description
of the clustering measured from the APM rich cluster redshift survey, which is
better fitted by models with more power at large scales. The amplitudes of the
rich cluster correlation functions measured from our models depend weakly on
cluster richness. Analytic calculations of the clustering of peaks in a
Gaussian density field overestimate the amplitude of the N-body cluster
correlation functions, but reproduce qualitatively the weak trend with cluster
richness. Our results suggest that the high amplitude measured for the
correlation function of richness class $R \geq 2$ Abell clusters is either an
artefact arising from incompleteness in the Abell catalogue, or an indication
that the density perturbations in the early universe were very non-Gaussian.
