The structure of mixed-alkali (Li,Na,K) molybdate and tungstate glasses with 55-62.5 mol% MoO3 and 53-65 mol% WO3 is studied using Raman spectroscopy, while the rheological behavior of the corresponding supercooled liquids is measured using parallel plate rheometry. The M-O (M = Mo,W) polyhedral units in these glasses are found to be similar to those characteristic of the crystalline alkali ortho- and pyro- molybdate and tungstate phases. The structure of glasses with ≤55 % MO3 is dominated by isolated [MO4]2− tetrahedra. Increasing MO3 content results in the formation of chain-like moieties of corner- and edge- sharing MO6 octahedra and MO4 tetrahedra. This compositional evolution of the glass structure is found to be consistent with the corresponding variation in Tg and viscosity of the parent supercooled liquids. Moreover, the low degree of structural connectivity of these liquids is manifested in rather high kinetic fragility index that is somewhat unprecedented in archetypal oxide systems.