A new relaxation mechanism is shown to arise from overdamped two-level
systems above a critical temperature T almost-equal-to 5 K, thus yie
lding an explanation for experimental observations in dielectric glass
es in the temperature range below the relaxation peak. Using the distr
ibution function of the tunnelling model for the parameters of the two
-level systems, both the linear decrease of the sound velocity and the
linear increase of the absorption up to the relaxation maximum, are q
uantitatively accounted for by our theory.