The crystal structures of the ammonium, 1, lithium, 2, potassium, 3, and cesium, 4, salts of a new nitrogen oxy anion, N3O4-, have been determined. In 1 there are two interpenetrating three-dimensional lattices linked by strong hydrogen-bonding interactions between all four ammonium protons and three of the four dinitramide oxygen atoms. Even though 2-4 have similar formula units each has a completely different structure characterized by differing coordination numbers and geometries. The structure of 2 is unique in that it is the only one containing a dinitramide ion in the C2 conformation predicted by nb initio studies to be the minimum energy conformation. There is good agreement between the predicted and experimental metrical parameters for the Ct conformer of the dinitramide anion.