The vibrational spectra of a number of transition metal tetra-oxo-complexes are reported for the first time, including those of salts containing the anions [RuO4]–; [MO4]2–(M = Mn, Fe, or Ru); [MO4]3–(M = Cr, Mn, Re, or Fe); and [MO4]4–(M = Ti, V, Cr, Mo, W, Fe, or Co). From these measurements and published data on the fundamental frequencies of other such ions we calculate force constants for most of the known transition-metal tetra-oxoanions. Raman data on [Cr18O4]2– and [W18O4]2– are also presented