A nonvolatile memory cell includes a layer (118) of a resistivity-switching metal oxide or nitride compound, the metal oxide or nitride compound including one metal, and a dielectric rupture antifuse (117) formed in series. The dielectric rupture antifuse may be either in its initial, non-conductive state or a ruptured, conductive state. The resistivity-switching metal oxide or nitride layer can be in a higher- or lower-resistivity state. By using both the state of the resistivity- switching layer and the antifuse to store data, more than two bits can be stored per memory cell.