Investigation of sulfur- and selenium-containing quasi-ternary systems Tl₂X–M^IIX–M^IVX₂ (M^II = Cd, Hg; M^IV = Si, Ge, Sn) by DTA and XRD methods at 520 K found the formation of twelve quaternary compounds, Tl₂HgSi(Ge,Sn)S₄, Tl₂PbSiS₄, Tl₂CdSi(Ge,Sn)Se₄, Tl₂HgSi(Ge,Sn)Se₄, Tl₂PbSi(Ge)Se₄, at the vertical sections Tl₂M^IVX₃–M^IIX, and seven compounds, Tl₂CdGe₃Se₈, Tl₂HgSi(Ge)₃S₈, Tl₂PbSi(Ge)₃S₈, Tl₂HgSi(Ge)₃Se₈, at the Tl₂M^IIM^IVX₄–M^IVX₂ sections. Additionally, series of analogous compounds Tl₂Cd(Hg)SiTe₄ of the 2-1-1-4 type and Tl₂Mg(Mn,Zn)Ge₃Se₈ of the 2-1-3-8 type, were obtained. The compounds of both 2-1-1-4 and 2-1-3-8 groups that form in the A^I₂Х–В^IIХ–D^IVX₂ system possess non-centrosymmetric crystal structure making them potential candidates for optical and other properties valuable for materials science. Similar quasi-ternary systems A^I₂Х–В^IIХ–D^IVX₂ feature quaternary phases, individual known representatives of which such as Li₂CdGeSe₄, Li₂CdSnSe₄, Cu₂CdGeSe₄, Cu₂CdSnSe₄, belong to diamond-like semiconductors and have already found use in non-linear optics and other fields of semiconductor applications. The structure of all quaternary compounds Tl₂M^IIM^IVX₄, except Pb-containing ones, was determined in isotropic approximation with the Tl₂HgGeTe₄ structure as model (tetragonal symmetry, space group I-42m), as well as six other tellurides Tl₂Mn(Cd,Hg)Ge(Sn)Te₄. Tl₂PbSiS₄ and Tl₂PbGeS₄ are isostructural and crystallize in the monoclinic symmetry, space group Р2₁/а. A family of compounds of the general formula Tl₂M^IIM^IV₃X₈ (M^II = Mg, Zn, Cd, Hg, Mn; M^IV = Ge; X = Se, Te) are analogous to the quaternary phases with alkaline metals α-K₂ZnSn₃S₈ and Cs₂M^IIM^IV₃Se₈ which crystallize in the orthorhombic symmetry, space group P2₁2₁2₁.