  We investigate the properties of clusters of galaxies in two cosmological
models using N-body simulations and the Press-Schecter (PS) theory. In the
first model, the initial power spectrum of density fluctuations is in the form
P(k) \propto k^{-2} at wavelengths \lambda<120h^{-1} Mpc. In the second model,
the initial linear power spectrum of density fluctuations contains a feature
(bump) at wavelengths \lambda \sim 30-60h^{-1} Mpc which correspond to the
scale of superclusters of galaxies. We examine the mass function, peculiar
velocities, the power spectrum and the correlation function of clusters in both
models for different values of the density parameter \Omega_0 and \sigma_8. The
results are compared with observations. We show that in many aspects the second
model fits the observed data better than the first simple power law model.
  We examine the linear theory predictions for the peculiar velocities of peaks
in the Gaussian field and compare these to the peculiar velocities of clusters
in N-body simulations. The numerical results show that the rms peculiar
velocity of clusters increases with cluster richness. The rms peculiar velocity
of small clusters is similar to the linear theory expectations, while the rms
peculiar velocity of rich clusters is higher than that predicted in the linear
theory (\sim 18% for clusters with a mean intercluster separation d_{cl} \sim
30h^{-1} Mpc).
