Standard solid-state methods produced black crystals of the compounds BaCu0.43(3)Te2 and BaAg0.77(1)Te2 at 1173 K; the crystal structures of each were established using single-crystal X-ray diffraction data. Both crystal structures are modulated. The compound BaCu0.43(3)Te2 crystallizes in the monoclinic superspace group P2(alpha beta 1/2)0, having cell dimensions of a = 4.6406(5) angstrom, b = 4.6596(5) angstrom, c = 10.362(1) angstrom, beta = 90.000(9)degrees, and Z = 2 and an incommensurate vector of q = 0.3499(6)b* + 0.5c*. The compound BaAg0.77(1)Te2 crystallizes in the orthorhombic P2(1)2(1)2(a00)000 superspace group with cell dimensions of a = 4.6734(1) angstrom, b = 4.6468(1) angstrom, c = 11.1376(3) angstrom, and Z = 2 and an incommensurate vector of q = 0.364(2)a*. The asymmetric unit of the BaCu0.43(3)Te2 structure comprises eight crystallographically independent sites; that for BaAg0.77(1)Te2 comprises four. In these two structures, each of the M (M = Cu, Ag) atoms is connected to four Te atoms to make two-dimensional layers of [MxTe4/4](n-) that are separated by layers of Ba atoms and square nets of Te. A Raman spectroscopic study at 298(2) K on a pelletized polycrystalline sample of BaAg0.8Te2 shows the presence of Ag-Te (83, 116, and 139 cm(-1)) and BaTe vibrations (667 and 732 cm(-1)). A UV-vis-NIR spectroscopic study on a powdered sample of BaAg0.8Te2 shows the semiconducting nature of the compound with a direct band gap of 1.0(2) eV, consistent with its black color. DFT calculations give a pseudo bandgap with a weak value of the DOS at the Fermi level.