  A simple model to investigate the long time dynamics of glass-formers is
presented and applied to study a Lennard-Jones system in supercooled and glassy
phases. According to our model, the point representing the system in the
configurational phase space performs harmonic vibrations around (and activated
jumps between) minima pertaining to a connected network. Exploiting the model,
in agreement with the experimental results, we find evidence for: i) stretched
relaxational dynamics; ii) a strong T-dependence of the stretching parameter;
iii) breakdown of the Stokes-Einstein law.
