We have recorded long spectral diffusion trajectories from individual LH2 pigment-protein complexes from the purple bacterium Rhodobacter sphaeroides at 1.4 K. From these data, the spectral cumulants of the absorption lines of individual, protein-embedded BChl a pigments have been evaluated. It appears that the first and second cumulants cannot be described by the predictions of the well tested standard two-level system (TLS) model for spectral diffusion in glasses. The results of the present study clearly show that there is a fundamental difference between the relaxation behavior of our test protein and that of glasses.