Ab initio band structure calculations were performed for the low-temperature modifications of the silver chalcogenides B-Ag2Se, B-Ag2Te and the ternary compound B-Ag3AuSe2 by the local spherical wave (LSW)method. Coordinated of the atoms of B-Ag2Se and B-Ag3AuSe2 were obtained from refinements using X-ray powder data. The structures are characterized by three, four and five coordinates of silver by the chalcogen, a linear coordination of gold by Se, and by metal-metal distances only slightly larger than in the metals. The band structure calculations show that B-Ag3AuSe2 is a semiconductor, while B-Ag2Se and B-Ag2Te are semimetals with an overlap of about 0.1-0.2 eV. The Ag 4d and Au 5d states are strongly hybridized with the chalcogen p states all over the valence bands. B-Ag2Se and B-Ag2Te have a very low DOS in the energy range from about -0.1 To +0.5 eV. The calculated effective mass B-Ag2Se is about 0.1-0.3 Me for electrons and 0.75 Me for holes, respectively.