  Using cosmological N-body simulations of critical (SCDM) and open ($\Omega =
0.3$, OCDM) cold dark matter models, we investigate evolution of cluster
galaxies. From our numerical simulation, we construct merging history trees of
the galaxies. By following their merging history, we show major merger
fractions of the galaxies in cluster forming regions is roughly proportional to
(1+z)^{4.5} at low redshifts (z < 2) and has a steep peak at $z \simeq 2.5$ and
$z \simeq 3$ in SCDM and OCDM, respectively. We also show that the cluster
galaxies are affected by tidal interaction after the clusters formed. Because
the formation redshift of the cluster in SCDM, z_{form} = 0.15, is much more
recent than that of the cluster in OCDM, z_{form} = 1.6, the cluster galaxies
in SCDM show more rapid evolution by tidal interactions from z = 0.5 than those
in OCDM.
