Ab initio band structure calculations were performed for the low-temperature modifications of the silver chalcogenides β-Ag 2Se, β-Ag 2Te and the ternary compound β-Ag 3AuSe 2 by the local spherical wave (LSW) method. Coordinates of the atoms of β-Ag 2Se and β-Ag 3AuSe 2 were obtained from refinements using X-ray powder data. The structures are characterized by three, four and five coordinations 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 β-Ag 3AuSe 2 is a semiconductor, while β-Ag 2Se and β-Ag 2Te 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. β-Ag 2Se and β-Ag 2Te have a very low DOS in the energy range from about −0.1 to +0.5 eV. The calculated effective mass β-Ag 2Se is about 0.1–0.3 m e for electrons and 0.75 m e for holes, respectively.