  The dynamical behavior of a kind of models with hierarchically constrained
dynamics is investigated. The models exhibit many properties resembling real
structural glasses. In particular, we focus on the study of time-dependent
temperature processes. In cooling processes, a phenomenon analogous to the
laboratory glass transition appears. The residual properties are analytically
evaluated, and the concept of fictive temperature is discussed on a physical
base. The evolution of the system in heating processes is governed by the
existence of a normal solution of the evolution equations, which is approached
by all the other solutions. This trend of the system is directly related to the
glassy hysteresis effects shown by these systems. The existence of the normal
solution is not restricted to the linear regime around equilibrium, but it is
defined for any arbitrary, far from equilibrium, situation.
