New triple molybdates Na25Cs8R5(MoO4)24 (R = Sc, In) were prepared as powders and ceramics by solid state reactions, and their single crystals were also obtained from melts by spontaneous crystallization. The structures were determined by single crystal XRD analysis. The electrical conductivity of ceramics was measured by impedance spectroscopy. The crystal structures were determined in monoclinic sp. gr. P21/c, a = 14.0069(3) Å, b = 12.6498(3) Å, c = 28.6491(6) Å, β = 90.007(1)° (Sc) and a = 14.0062(2) Å, b = 12.6032(2) Å, c = 28.7138(4) Å, β = 90.001(1)° (In). Together with triclinic Na25Cs8Fe5(MoO4)24, the titled compounds form a distinctive family of pseudo-orthorhombic alluaudite-related structures with the parent sp. gr. Pbca. Its structural features are alluaudite-like polyhedral layers composed of pairs of edge-shared (R, Na)O6 and NaO6 octahedra connected by bridging MoO4 tetrahedra. The layers are joined together by means of interlayer MoO4 tetrahedra, thus forming open 3D frameworks with cavities filled with Cs+ and Na+ ions. The manner of stacking layers is somewhat different from the alluaudite type. The compounds undergo phase transitions at 668 (Sc) and 725 (In) K accompanied by an abrupt increase of electrical conductivity presumably Na+-ionic in nature. Above these transitions, the conductivity is as high as 10-3 S cm-1, which makes Na25Cs8R5(MoO4)24 (R = Sc, In) promising solid state electrolytes.