The structures of single crystals of CuIn3Se5 and CuIn5Se8 ternary compounds have been studied by X-ray diffraction for the first time. The unit cell parameters of CuIn3Se5 and CuIn5Se8 crystals are determined. It is established that CuIn3Se5 has a thiogallate lattice with c = 2a, which leads to the domain structure formation. CuIn5Se8 has a hexagonal lattice and exhibits cleavage along the (001) plane. Relationships between the atomic composition and crystal structure of these new ternary semiconductor compounds are discussed.