  A dynamical theory is constructed to describe spectral diffusion in glasses
in the temperature range near 1 Kelvin on long time scales. The theory invokes
interacting tunneling centers (TLS) which provide an excess contribution to the
spectral hole width which qualitatively accounts for the deviation from
standard logarithmic line broadening observed by Maier et al. [Phys. Rev. Lett.
76, 2085 (1996)]. Alternative explanation schemes of the nonlogarithmic line
broadening, avoiding interacting TLS, are discussed. We devise experimental
tests which could be used to access the validity of the proposed theories.
