  We present simulations of the cluster distribution in several dark matter
models, using an optimized version of the truncated Zel'dovich approximation
(TZA). We compare them with N-body cluster simulations and find that the TZA
provides a very accurate description of the cluster distribution as long as
fluctuations on the cluster mass scale are in the mildly non-linear regime. The
simulated dark matter models are: Standard CDM (SCDM), Tilted CDM (TCDM) with
n=0.7, Cold+Hot DM (CHDM) with 30% of hot component, low Hubble constant
(h=0.3) CDM (LOWH) and a spatially flat low-density CDM model with
\Omega_0=0.2. We compare the simulations with a redshift sample of Abell/ACO
clusters, using the integral of the 2-point correlation function and the
probability density function. We find that the best models at reproducing the
data are CHDM and LCDM. All the other models are ruled out. The reduced
skewness S_3 is fairly constant with S_3=1.9, independent of the DM model and
consistent with observational data. The abundances of clusters predicted using
the Press--Schechter theory provide strong constraints: only the CHDM, LOWH and
LCDM models appear to produce the correct number-density of clusters.
