  We study the relaxation process in normal and anomalous diffusion regimes for
systems described by a generalized Langevin equation (GLE). We demonstrate the
existence of a very general correlation function which describes the relaxation
phenomena. Such function is even; therefore, it cannot be an exponential or a
stretched exponential. However, for a proper choice of the parameters, those
functions can be reproduced within certain intervals with good precision. We
also show the passage from the non-Markovian to the Markovian behaviour in the
normal diffusion regime. For times longer than the relaxation time, the
correlation function for anomalous diffusion becomes a power law for broad-band
noise.
