K₂Mo₄O₁₃ crystallises in the triclinic system, space group P, with Z= 2 in a unit cell of dimensions a= 7·972, b= 8·352, c= 10·994 Å, α= 119·4, β= 62·7, and γ= 109·8°. Its structure, determined by three-dimensional Patterson and Fourier methods and refined by least-squares techniques, contains subunits of eight distorted MoO₆ octahedra sharing edges, joined by a common edge to form infinite chains, with adjacent chains having no common oxygen atoms. The potassium ions occupy irregular eight-co-ordinate interchain sites. Rb₂Mo₄O₁₃ is isomorphous with K₂Mo₄O₁₃. The tetramolybdate chain structure is compared with those of some other anhydrous polymolybdates(VI), and the similarity of the subunit of eight octahedra to the basic units found in a number of complex molybdates, and to the hepta- and octa-molybdate polyanions, is discussed. The possible existence of polyanions in molybdate melts is considered, and the ability to predict polymolybdate structures from i.r. absorption spectra critically assessed.