The theoretical feasibility of sulfide ion transport in phases based on MeLn₂S₄ (Me = Ca, Ba; Ln = Sm, Pr) is considered. Regions of solid solutions on the basis of ternary compounds are determined. A systematic investigation of phases is performed with the application of a variety of electrochemical methods, specifically, the conductimetry, emf in chemical concentration cells with and without transport, and Tubandt methods.