We study the ability of COBE-normalized CDM models to reproduce observed properties of the distribution of galaxies and clusters using N-body numerical simulations .
We analyze the galaxy-galaxy and cluster-galaxy two-point correlation functions , \xi _ { gg } and \xi _ { cg } , in open ( \Omega _ { 0 } = 0.4 , \Omega _ { \Lambda } = 0 , \sigma _ { 8 } = 0.75 ) , and flat ( \Omega _ { 0 } = 0.3 , \Omega _ { \Lambda } = 0.7 , \sigma _ { 8 } = 1.05 ) CDM models which both reproduce the observed abundances of rich clusters of galaxies .

To compare models with observations we compute projected cross-correlation functions \omega _ { gg } and \omega _ { cg } to derive the corresponding \xi _ { gg } and \xi _ { cg } .
We use target galaxies selected from Las Campanas Redshift Survey , target clusters selected from the APM Cluster Survey and tracer galaxies from the Edinburgh Durham Sky Survey catalog .

We find that the open model is able to reproduce the observed \xi _ { gg } , whereas the flat model needs antibias in order to fit the observations .
Our estimate of \xi _ { cg } for the APM cluster sample analyzed is consistent with a power-law \xi _ { cg } = ( { r \over r _ { 0 } } ) ^ { \gamma } with r _ { 0 } = 10.0 \pm 0.7 h ^ { -1 } Mpc and \gamma \simeq - 2.1 .
For the open and flat-antibiased CDM models explored we find the corresponding cluster-galaxy correlation lengths 6.5 \pm 0.7 h ^ { -1 } Mpc and 7.2 \pm 0.5 h ^ { -1 } Mpc respectively , significantly lower than the observed value .
Our results indicate that COBE-normalized CDM models are not able to reproduce the spatial cross-correlation of clusters and galaxies .