Spectral diffusion (SD) in PMMA doped with H 2 -TPP is investigated at 4.2K on a time scale of 3–106s via optical hole burning. Two contradictory results – within the framework of the TLS model – are obtained. The first one is the absence of aging effects which puts the upper limit for the TLS relaxation times to tens of minutes. The second one is an intensive superlogarithmic SD on the whole time scale of the experiment, which evidences the presence of very slow relaxations, independent of the sample history on a time scale of up to 2 months. The presented results provide clear evidence of a deviation of SD behavior from the TLS model predictions at moderately low temperatures. The concept of structural relaxations is applied for a qualitative interpretation of the experimental data.