  We present a dynamical description of slow relaxation processes based on the
extension of Onsager's fluctuation theory to systems in local
quasi-equilibrium. A non-Markovian Fokker-Planck equation for the conditional
probability density is derived and from it we obtain the relaxation equation
for the moments. We show that the fluctuation-dissipation theorem can be
formulated in terms of the temperature of the system at local
quasi-equilibrium. Our theory may be applied to a wide variety of systems
undergoing slow relaxation. We discuss in particular slow dynamics in glassy
systems and Brownian motion in a granular gas.
