We investigated the spectra of a large number of single tetra-tert-butylterrylene molecules embedded in an amorphous polyisobutylene matrix and analyzed the distributions of their linewidths (widths of single spectral peaks). The measurements were performed at 2, 4.5, and 7 K. This is a temperature region, where the standard two-level system (TLS) model of low-temperature glasses begins to fail. At T=2 K the temporal behavior (history of frequency jumps) of most of the measured spectra and their linewidth distributions were found to be consistent with the TLS model. At higher temperatures the main features of individual spectra (number of spectral peaks, temperature variation of peak widths, ratio of intensities of different peaks, etc.) still appear consistent with the predictions of this model. An increase of temperature leads mainly to the broadening of spectral peaks. A detailed analysis of the linewidth distributions reveals deviations from a standard TLS model at T=4.5 and 7 K. This difference is attributed to the influence of quasi-local low-frequency modes (LFM) of the amorphous matrix. By comparing the measured linewidth distributions with computer simulations, we quantitatively determined the LFM contribution to the single-molecule spectra in our dye-matrix system at different temperatures. (C) 2003 American Institute of Physics.