A model of the TlGaSe,-I band structure of the monoclinic modification is proposed. The monoclinic modification of TIGaSe,-I is considered as a deformed tetragonal one. The band structure of the metastable tetragonal modification of TlGaSe,-II is calculated by the pseudopotential method. The irreducible representations of the DiZ group (TlGaSe,-11) are expanded in irreducible representations of the ( 3: group (TlGaSe,-I). It is found that the top of the valence band is located a t the point Y (0,2n/b,, 0) of the TIGaSe,-I Brillouin zone and is formed from band states N,, N,, of the tetragonal modification. The bottom of the conduction band is located a t the point I' of the TIGaSe,-I Brillouin zone and is formed from T4 states. An additional extremum of the valence and conduction bands is located a t the points I'(A,) and Y(N,, N8), respectively. An interpretation of the absorption spectra of TIGaSe,-I near the fundamental edge is proposed. npeAnomeIla MOAei JIb 30HHOB CTPYHTYPLI TIGaSe,-I MOHOKJIHHHOt MOAH@HIcaWWi. MomHnHHIIaR MOAH@HKaL[HfI TIGaSe,-I paccMoTpeHa KaIC Ae@OpMHpOBaHHaR TeTpa-rOHaJILI-IaFI. 30HHaR CTpyHTypa MeTacTa6HJrbHOl% TeTparOHaiJIbHOI% MOnH@HX3UEzH BOAHMLIX IIpencTaBJIeHHHi% rpynnLI D; : (TlGaSe,-11) I I O HeIIpHBOiTHMLIM IIpeaCTaB-JIeIlEzfIM rpyniIM c: (TIGaSe,-I). HaBAeHo, YTO JIOTOJIOH B2IJIeHTHOg 30HLI pacnoJIomeH B TOYKe Y (0, 2nlbm, 0) 30IlbI EPHJIJII03Ha TlGaSe,-I Ez 06pa30BaH 113 30HHbIX COCTORHHg N,, N4 TeTpWOHaJILHOa MOAH@HKaUHM. AH0 30HLI lIpOB0nHMOCTH paCIIOJIOmeH0 B TOYHe I? 8 O H h I EpkIJIJIIO3Ha TlGaSe,-I H 06pa30sa~o H 3 COCTOHHHH T,. ~OIlOJIHHTenbHbIs 3HCTpeMYM B&TIel-ITHOfi 30HLI JIOKaJIH30BaH B TOYHe I'(A,), a 30IlLI IIpOBOAHMOCTH B B6nH3Ez @yHnaMeIITaJIbHOrO R p a H . TlGaSe,-II paccwmar-la MeToAoM nceBAonoTeiwnana. IIponeReHo p a m o m e~~e n e n p~-Towe Y(N,, N,) . IIpeAnomeHa HwrepnpeTaUm cneKTpoB nornolueam TIGaSe,-I