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As results of a powder XRD study of sintered samples of the systems Na 2 MoO 4 – M MoO 4 ( M = Co, Cd) quenched in air from 873 K, the literature data on the phase formation and homogeneity ranges of nonstoichiometric double molybdates in these systems were corrected. The compounds are monoclinic alluaudite-type Na 4-2 x Co 1+ x (MoO 4 ) 3 (0.05 ≤ x ≤ 0.30) and Na 4-2 x Cd 1+ x (MoO 4 ) 3 (0.10 ≤ x ≤ 0.40), orthorhombic lyonsite-type Na 2-2 y Co 2+ y (MoO 4 ) 3 (0.05 ≤ y ≤ 0.25), and triclinic Na 2-2 z Co 2+ z (MoO 4 ) 3 (0.10 ≤ z ≤ 0.40) of the Na 2 Mg 5 (MoO 4 ) 6 type. The temperature of the orthorhombic-to-triclinic phase transition was found to be 943 ± 10 K. Crystal structures of the alluaudite-type double molybdates (space group C 2/c, Z = 4) with cobalt, manganese, and cadmium were determined. According to the atomic position occupations, the compositions for the crystals were found as Na 3.36 Co 1.32 (MoO 4 ) 3 ( a = 12.6381(3), b = 13.4888(4), c = 7.1244(2) Å, β = 112.127(1)° , R = 0.0207), Na 3.13 Mn 1.43 (MoO 4 ) 3 ( a = 12.7387(3), b = 13.6716(4), c = 7.1904(2) Å, β = 112.404(1)°, R = 0.0166), and Na 3.72 Cd 1.14 (MoO 4 ) 3 ( a = 12.804(3), b = 13.913(3), c = 7.326(2) Å, β = 112.63(1)° , R = 0.0158). The crystal chemistry and compositions of the alluaudite-type molybdates and tungstates were considered and mainly one-dimensional character of the sodium-ion transport was shown for them. The measured values of the ionic conductivity of sintered samples of Na 3.6 M 1.2 (MoO 4 ) 3 ( M = Mg, Ni, Zn, Cd) and Na 3.6 Mg 1.2 (WO 4 ) 3 exceeds 10 −3 S cm −1 at 673 K. [ABSTRACT FROM AUTHOR]