Lithium magnesium molybdates of the general formula Li_2−2xMg_2+x(MoO₄)₃, for 0 ≤ x ≤ 0.3, have been synthesized and their structure and lithium ion conductivity investigated. Determination of crystal structure of one of the members, Li₂Mg₂(MoO₄)₃, has revealed a three-dimensional framework consisting of metal–oxygen octahedra and trigonal prisms (where Li and Mg reside) which are interconnected by MoO₄ tetrahedra. Although the framework is three-dimensional, lithium-ion conductivity appears to be restricted to the one-dimensional channels formed by interconnected trigonal prisms. Isotypic molybdates, Li₃M(MoO₄)₃ (M = Cr, Fe), where lithium ions occupy exclusively the trigonal prismatic channels, exhibit a higher lithium ion conductivity than Li_2−2xMg_2+x(MoO₄)₃, lending support to the idea that the conductivity is one-dimensional in these materials. ⁷Li NMR spectral data are consistent with this interpretation.