  A star with main sequence mass greater than $25\sim 30\msun$ may collapse to
a black hole of about 10 $\msun$ at the final stage of the evolution. About an
order of 1\% of stellar mass is likely to be in form of such black holes in
galaxies. We have examined the dynamics of two-component stellar systems
composed of 0.7 $\msun$ main-sequence stars, representing the old population of
stars whose main-sequence lifetimes are longer than the Hubble time, and a
small fraction of 10 $\msun$ black holes. The dynamical friction leads to the
segregation of black holes to the core and the core collapse takes place among
the black holes in a time scale much shorter than that required for a single
component cluster. The ultimate evolution of the two-component stellar system
depends on the role of three-body binaries formed among the black holes. For a
system with $v\gta 100\kms$ binaries merge by gravitational radiation at some
hardness instead of being ejected. The critical hardness, at which the
collision time and the merger time become comparable, determines the efficiency
of the binary as a heat source. The efficiency is found to be inversely
proportional to the velocity dispersion. For the clusters without serious
reduction in heating efficiency (i.e., velocity dispersion well below 500
$\kms$), heating by three-body binaries have the effect of stopping the
core-collapse. The cluster
