  We use N-body simulations to study evolution of galaxy clusters over the
redshift interval 0 <= z <= 0.5 in cosmological models with a mixture of cold
and hot dark matter (CHDM). Four different techniques are utilized: the
cluster-cluster correlation function, axial ratios and quadrupoles of the dark
matter distribution in individual clusters, and virial properties. We find that
the correlation function for clusters of the same mass limit was larger and
steeper at high redshifts. The slope increases from 1.8 at z=0 to 2.1 at z=0.5.
Comoving correlation length r_c scales with the mass limit M within comoving
radius 1.5 h^-1 Mpc and the redshift z as r_c ~= 20(1+z)(M/M_*)^1/3, where M_*
= 3*10^14 h^-1 M_sun. When the correlation length is normalized to the mean
cluster separation d_c, it remains almost constant: r_c~=(0.45-0.5) d_c. For
small masses (M_clust <2*10^14 h^-1 M_sun) there is an indication that r_c goes
slightly above the relation with the constant of proportionality being ~=
0.55-0.6. Anisotropy of density distribution in a cluster shows no change over
redshift with axial ratios remaining constant around 1.2. In other words,
clusters at present are as elongated as they were at the epoch of their first
appearance. While the anisotropy of clusters does not change with time, the
density profile shows visible evolution: the slope of density profile changes
from gamma ~= -3.5 at z=0.5 to gamma ~= -2.5 at the present. We find that the
core of a cluster remains essentially the same over time, but the density of
the outlying regions increases noticeably. The virial relation M ~ v^2 is a
good approximation, but there is a large fraction of clusters with peculiar
velocities greater than given by this relation, and clusters with the same rms
velocities have smaller masses in the past, a factor of 2 at z=0.5.
