  We study the Langevin equation for a single harmonic saddle as an elementary
model for the beta-relaxation in supercooled liquids close to Tc. The input of
the theory is the spectrum of the eigenvalues of the dominant stationary points
at a given temperature. We prove in general the existence of a time-scale
t_eps, which is uniquely determined by the spectrum, but is not simply related
to the fraction of negative eigenvalues. The mean square displacement develops
a plateau of length t_eps, such that a two-step relaxation is obtained if t_eps
diverges at Tc. We analyze the specific case of a spectrum with bounded left
tail, and show that in this case the mean square displacement has a scaling
dependence on time identical to the beta-relaxation regime of Mode Coupling
Theory, with power law approach to the plateau and power law divergence of
t_eps at Tc.
