Ternary TlGaSe 2 compounds are ferroelectric semiconductors possessing a complex layered structure. Each layer of a single TlGaSe 2 crystal comprises strongly covalently bonded GaSe 4 tetrahedral units and exhibits overall anionic character. Weak interlayer bonds in the crystal are ensured by the Tl + cations stacked in the trigonal cavities between the layers. The elementary 32 atoms cell of TlGaSe 2 has monoclinic symmetry and belongs to the C 2/c (C 6 2h ) space group [1]. It is known that the compound undergoes two-phase transformations at temperatures between 105 and 120 K [2,3]. Unique optical properties of the semiconductor dictated by its structural complexity received a great deal of attention for applications in photoelectronics [4].In the past, several works were dedicated to the fundamental optical absorption of TlGaSe 2 [5-10]. Parameters extracted in these studies primarily concern the direct band gap character of the compound. Information obtained about the simultaneous indirect optical transitions, on the other hand, remains highly inconsistent and controversial due to differences in sample quality and measurement arrangements. In addition, most of the detected spectra exhibit poorly resolved absorption features [8,9]. To the best of our knowledge, the fine absorption structure involving assisting phonons has been only detected in narrow 2.05-2.08 eV spectral range [6]. In this paper we present highresolution absorption measurements at different temperatures performed in the high-quality TlGaSe 2 crystals. The analysis of low temperature spectrum provides us a clue to insight into the role of indirect optical transitions.The data reported here refer to a set of crystals synthesized by the Bridgman method from high-purity elements taken in stoichiometric proportions. Samples of a few millimetres thickness and mirror-like surfaces were obtained by cleaving the crystals along the layers. For absorption measurements along these layers (see text below) side surfaces of specimens were polished to optical quality. The examined samples showed weak p-type conduction at room temperature while their optical trapping concentration was less than 10 16 cm -3 . More detailed results on sample structure and free carrier dynamics are presented elsewhere [11].Optical transmission of samples was measured using a dual beam spectrometer with a resolution not less than 1 nm equipped with a xenon flash tube. Such apparatus simultaneously acquires data from the sample and reference detectors avoiding fluctuations of the lamp brightness. Non-polarized light was used in the experiments. During measurements the samples were cooled down to helium temperatures using a close cycle cryostat. The absorption coefficient, α, has been calculated taking into account multiple reflections from parallel surfaces. We also accounted for a small increase of reflectivity versus photon energy R(E) recorded for E⊥c polarization at room temperature [8]. For low temperatures this dependence was uniformly shifted in energy according to the blue...