The quasi-ternary system Cu₂Se-In₂Se₃-CuI has been investigated by x-ray diffraction and differential thermal analysis. The isothermal section at 770 K and the liquidus surface projection of the system have been built. For the first time, the primary crystallization regions, and the coordinates of the invariant and monovariant equilibria have been determined. In the system, the regions of the solid solutions based on the binary, ternary, and quaternary compounds have been investigated. The formation of the CuIn₂Se₃I quaternary compound, which melts congruently at 1213 K and has a homogeneity region of 15 and 9 mol.% CuI within the composition triangle has been established. For the first time, the crystal structures of CuGa₂Te₃I and AgGa₂Te₃Br compounds have been studied using a powder method. They crystallize in the tetragonal symmetry, Space Group I-4, a = 5.9147(4) Å, c = 11.952(2) Å for CuGa₂Te₃I; a = 6.2977(3) Å, c = 11.9473(7) Å for AgGa₂Te₃Br compound, respectively. The connection of their structures with the structures of the defective diamond-like semiconductors has been discussed.