In view of the search for and understanding of new materials for energy storage, the Li-Ag-Ge phase diagram has been investigated. High-temperature syntheses of Li with reguli of premelted Ag and Ge led to the two new compounds Li2AgGe and Li2.80-xAgGe2 (x = 0.27). The compounds were characterized by single-crystal X-ray diffraction. Both compounds show diamond-polytype-like polyanionic substructures with tetrahedrally coordinated Ag and Ge atoms. The Li ions are located in the channels provided by the network. The compound Li2AgGe crystallizes in the space group R (3) over barm (No. 166) with lattice parameters of a = 4.4424(6) angstrom and c = 42.7104(6) angstrom. All atomic positions are fully occupied and ordered. Li2.80-xAgGe2 crystallizes in the space group I41/a (No. 88) with lattice parameters of a = 9.7606(2) angstrom and c = 18.4399(8) angstrom. The Ge substructure consists of unique (1)(infinity)[Ge-10] chains that are interconnected by Ag atoms to build a three-dimensional network. In the channels of this diamond-like network, not all of the possible positions are occupied by Li ions. Li atoms in the neighborhood of the vacancies show considerably enlarged displacement vectors. The occurrence of the vacancy is traced back to short Li-Li distances in the case of the occupation of the vacancy with Li. Both compounds are not electron-precise Zintl phases. The density of states, band structure, and crystal orbital Hamilton population analyses of Li2.80-xAgGe2 reveal metallic properties, whereas a full occupation of all Li sites leads to an electron-precise Zintl compound within a rigid-band model. Li2AgGe reveals metallic character in the ab plane and is a semiconductor with a small band gap along the c direction.