  We investigate the properties of clusters of galaxies in the $\Lambda$CDM
models with a steplike initial power spectrum. We examine the mass function,
the peculiar velocities and the power spectrum of clusters in models with
different values of the density parameter $\Omega_0$, the normalized Hubble
constant h and the spectral parameter p, which describes the shape of the
initial power spectrum. The results are compared with observations. We also
investigate the rms bulk velocity in the models, where the properties of
clusters are consistent with the observed data. We find that the power spectrum
of clusters is in good agreement with the observed power spectrum of the
Abell-ACO clusters, if the spectral parameter p is in the range p=0.6-0.8. The
power spectrum and the rms peculiar velocity of clusters are consistent with
observations only if $\Omega_0<0.4$. The $\Omega_0=0.3$ models are consistent
with the observed properties of clusters, if h=0.50-0.63. For h=0.65, we find
that $\Omega_0=0.20 -0.27$.
