  Stage-2 CoCl$_{2}$-GIC is a spin ceramic and shows hierarchical successive
transitions at $T_{cu}$ (= 8.9 K) and $T_{cl}$ (= 7.0 K) from the paramagnetic
phase into an intra-cluster (two-dimensional ferromagnetic) order with
inter-cluster disorder and then to an inter-cluster (three-dimensional
antiferromagnetic like) order over the whole system. The nature of the
inter-cluster disorder was suggested to be of spin glass by nonlinear magnetic
response analyses around $T_{cu}$ and by studies on dynamical aspects of
ordering between $T_{cu}$ and $T_{cl}$. Here, we present a further extensive
examination of a series of time dependence of zero-field cooled magnetization
$M_{ZFC}$ after the aging protocol below $T_{cu}$. The time dependence of the
relaxation rates $S_{ZFC}(t) = (1/H)dM_{ZFC}(t)/d\ln t$ dramatically changes
from the curves of simple spin glass aging effect below $T_{cl}$ to those of
two peaks above $T_{cl}$. The characteristic relaxation behavior apparently
indicates that there coexist two different kinds of glassy correlated regions
below $T_{cu}$.
