  Using a set of $\pppm$ simulation which accurately treats the density
evolution of two components of dark matter, we study the evolution of clusters
in the Cold + Hot dark matter (CHDM) model. The mass function, the velocity
dispersion function and the temperature function of clusters are calculated for
four different epochs of $z\le 0.5$. We also use the simulation data to test
the Press-Schechter expression of the halo abundance as a function of the
velocity dispersion $\sigma_v$. The model predictions are in good agreement
with the observational data of local cluster abundances ($z=0$). We also
tentatively compare the model with the Gunn and his collaborators' observation
of rich clusters at $z\approx 0.8$ and with the x-ray luminous clusters at
$z\approx 0.5$ of the {\it Einstein} Extended Medium Sensitivity Survey. The
important feature of the model is the rapid formation of clusters in the near
past: the abundances of clusters of $\sigma_v\ge 700\kms$ and of $\sigma_v\ge
1200 \kms$ at $z=0.5$ are only 1/4 and 1/10 respectively of the present values
($z=0$). Ongoing ROSAT and AXAF surveys of distant clusters will provide
sensitive tests to the model. The abundance of clusters at $z\approx 0.5$ would
also be a good discriminator between the CHDM model and a low-density flat CDM
model both of which show very similar clustering properties at $z=0$.
