The phase equilibria in the system Ag–Pd–Te were studied by the technique of using an evacuated silica glass tube at 350° and 450°C. Five ternary phases were synthesized: sopcheite (Pd3Ag4Te4), lukkulaisvaaraite (Pd14Ag2Te9), telargpalite (Pd2−xAg1+xTe) and the previously unknown phases Pd7.5−xAg0.5+xTe3 and Pd2+xAg2−xTe. The synthetic telargpalite has a compositional range from 26 to 29 wt.% Ag, with the formula Pd2−xAg1+xTe, where x varies from 0.09 to 0.22. The phase Pd2+xAg2−xTe has a compositional range from 34 to 35 wt.% Ag, where x varies from 0.18 to 0.24. The phase Pd7.5−xAg0.5+xTe3 forms a solid solution from 4 to 11 wt.% Ag, where x varies from 0.02 to 0.83. Phases Pd20Te7 and Pd13Te3 dissolve up to 3.5 and 2 wt.% Ag, respectively. Other binary palladium tellurides do not dissolve Ag. The phase Pd3Ag4Te4, an analogue of the mineral sopcheite, forms a stable association with hessite and kotulskite it also coexists with lukkulaisvaaraite. Sopcheite is stable up to 383°C. Natural occurrences of hessite, kotulskite and lukkulaisvaaraite together in equilibrium indicate formation above this temperature. Phase relations defined the mineral assemblages that can be expected to occur in nature. The phase Pd7.5−xAg0.5+xTe3 potentially represents a new mineral; it will probably be found in association with lukkulaisvaaraite and telargpalite or telluropalladinite, among other platinum-group minerals. The phase Pd2+xAg2−xTe can be found in association with telargpalite. Mineral assemblages defined in this study can be expected in Cu-Ni-PGE mineral deposits, associated with mafic and ultramafic igneous rocks, particularly in mineralized zones with known silver-palladium tellurides.