Two lithium oxonitridophosphate materials are computationally examined and found to be promising solid electrolytes for possible use in all solid-state batteries having metallic Li anodes – Li14P2O3N6 and Li7PN4. The first principles simulations are in good agreement with the structural analyses reported in the literature for these materials and the computed total energies indicate that both materials are stable with respect to decomposition into binary and ternary products. The computational results suggest that both materials are likely to form metastable interfaces with Li metal. The simulations also find both materials to have Li ion migration activation energies comparable or smaller than those of related Li ion electrolyte materials. Specifically, for Li7PN4, the experimentally measured activation energy can be explained by the migration of a Li ion vacancy stabilized by a small number of O2− ions substituting for N3− ions. For Li14P2O3N6, the activation energy for Li ion migration has not yet been experimentally measured, but simulations predict it to be smaller than that measured for Li7PN4.