Embodiments of the invention include nonvolatile memory elements and memory devices comprising the nonvolatile memory elements. Methods for forming the nonvolatile memory elements are also disclosed. The nonvolatile memory element comprises a first electrode layer, a second electrode layer, and a plurality of layers of an oxide disposed between the first and second electrode layers. One of the oxide layers has linear resistance and substoichiometric composition, and the other oxide layer has bistable resistance and near-stoichiometric composition. Preferably, the sum of the two oxide layer thicknesses is between about 20 Å and about 100 Å, and the oxide layer with bistable resistance has a thickness between about 25% and about 75% of the total thickness. In one embodiment, the oxide layers are formed using reactive sputtering in an atmosphere with controlled flows of argon and oxygen.