The title compounds were prepared from the elements in evacuated silica tubes at 650 degrees C, followed by slow cooling. Ba2Ag4Se5 forms a new structure,type, space group C2/m, with a = 16.189(2) angstrom, b = 4.5528(6) angstrom, c 9.2500(1) angstrom, beta = 124.572(3)degrees, and V = 561.4(1) angstrom(3) (Z = 2). A maximum of 44% of the Ag atoms may be replaced with Cu atoms without changing the structure type. The crystal structure is composed of Ag4Se54- layers, interconnected via the Ba2+ cations. The Ag atoms show irregular [3 + 1] coordination by the Se atoms, and the Ba atoms are located in capped square antiprisms formed by Se atoms. Most intriguing is the unprecedented occurrence of linear Se-3(4-) units. According to the formulation (Ba2+)(2)(Ag+)(4)Se-3(4-)(Se2-)(2), this selenide is electron-precise with eight positive charges equalizing the eight negative charges. Electronic structure calculations indicated the presence of a band gap, as was experimentally confirmed: the electrical conductivity measurement revealed a gap of 0.6 eV for Ba2CuAg3Se5.