  We derive scaling limit results for the Random Hopping Dynamics for the
cascading two-level GREM at low temperature at extreme time scales. It is known
that in the cascading regime there are two static critical temperatures. We
show that there exists a (narrow) set of fine tuning temperatures; when they
lie below the static lowest critical temperature, three distinct dynamical
phases emerge below the lowest critical temperature, with three different types
of limiting dynamics depending on whether the temperature is (well) above or
below, or at a fine tuning temperature, all of which are given in terms of K
processes. We also derive scaling limit results for temperatures between the
lowest and he highest critical ones, as well as aging results for all the
limiting processes mentioned above, by taking a second small time limit.
