  We first present the results of numerical simulations on formation processes
and physical properties of old globular clusters (GCs) located within clusters
of galaxies (``intracluster GCs'') and in between clusters of galaxies
(``intercluster GCs''). Our high-resolution cosmological simulations with
models of GC formation at high redshifts ($z>6$) show that about 30 % of all
GCs in a rich cluster can be ragarded as intracluster GCs that can freely drift
being trapped by gravitational potential of the cluster rather than by the
cluster member galaxies. The radial surface density profiles of the simulated
intracluster GCs are highly likely to be flatter than those of GCs within
cluster member galaxies. We also find that about 1% of all GCs formed before
$z>6$ are not located within any virialized halos and can be regarded as
``intercluster'' (or ``intergalactic'') GCs. We discuss the dependences of
physical properties of intracluster and intercluster GCs on the initial density
profiles of GCs within low-mass dark matter halos at high redshifts ($z>6$).
