Phase diagrams have been determined for the systems MI+AgI (M = Na, K, Rb, Cs, Tl or NH4), MBr+AgBr (M = K, Rb or Cs) and MI+CuI (M = K or Rb). A group of isomorphous compounds MAg4I5(M = K, Rb, NH4) with exceptionally high ionic conductivity has been identified. At 20°C the conductivity of polycrystalline RbAg4I5 is 0.124 ± 0.006 ohm–1 cm–1, i.e., higher than the ionic conductivity of any other known solid. At this temperature RbAg4I5 is stable, but KAg4I5 and NH4Ag4I5 slowly disproportionate to AgI and K2AgI3 or (NH4)2AgI3. The ternary system KI+RbI+AgI contains a complete range of solid solutions (K,Rb) Ag4I5. Analogous bromides have not been found, but a compound KCu4I5 is stable between 257 and 332°.