Resistive switching in nonvolatile, two terminal organic memories can be due to the presence of a native oxide layer at an aluminum electrode. Reproducible solid state memories can be realized by deliberately adding a thin sputtered Al2O3 layer to nominal electron-only, hole-only, and bipolar organic diodes. Before memory operation, the devices have to be formed at an electric field of 10^9 V/m, corresponding to soft breakdown of Al2O3. After forming, the structures show pronounced negative differential resistance and the local maximum in the current scales with the thickness of the oxide layer. The polymer acts as a current limiting series resistance.