In the quasi-binary systems Li3N-MI (M=Li, Na, K, Rb) new intermediate compounds 3Li(3)N-MI? were synthesized by a solid-stare reaction between Li3N and MI at 600 degrees C., They were isomorphous and had a tetragonal unit cell. Their sintered bodies exhibited lithium-ion conductivity of 1.1 x 10(-4)-7.0 X 10(-5) S cm(-1) at room temperature. The grain boundary resistances were negligibly small because of their goad sinterability. The decomposition voltages were approximately 2.5-2.8 V, much higher than that of Li3N. Even the compacts of the powdered compounds showed total conductivities more than 10(-5) S cm(-1). This allowed the cell construction of the solid-state lithium-ion cell, C/3Li(3)N-KI/LiTiS2,, simply by pressing the powdered electrolyte and electrode materials. The cell was able to charge and to discharge at a constant current of 15 mu A cm(-2) at room temperature: however, severe polarization in the positive electrodes limited the charge/discharge performance.