  Magnetizations are introduced to the Generalized Random Energy Model (GREM)
and numerical simulations on ac susceptibility is made for direct comparison
with experiments in glassy materials. Prominent dynamical natures of spin
glasses, {\it i.e.}, {\em memory} effect and {\em reinitialization}, are
reproduced well in the GREM. The existence of many layers causing continuous
transitions is very important for the two natures. Results of experiments in
other glassy materials such as polymers, supercooled glycerol and orientational
glasses, which are contrast to those in spin glasses, are interpreted well by
the Single-layer Random Energy Model.
