J-aggregates and monomers of a thiacarbocyanine derivative are investigated in glassy matrices by spectral hole burning. The temperature dependence (at T 4.6-20 K) of the width of the hole burnt in the absorption band of aggregates differs qualitatively from that of the hole in the absorption band of monomers. The hole width for J-aggregates does not depend on temperature below 9 K and is equal to 3.3 cm(-1). This residual hole width is suggested to be determined by exciton-phonon scattering with phonon emission.