A non-volatile nanotube switch and memory arrays constructed from these switches are disclosed. A non-volatile nanotube switch includes a conductive terminal and a nanoscopic element stack having a plurality of nanoscopic elements arranged in direct electrical contact, a first comprising a nanotube fabric and a second comprising a carbon material, a portion of the nanoscopic element stack in electrical contact with the conductive terminal. Control circuitry is provided in electrical communication with and for applying electrical stimulus to the conductive terminal and to at least a portion of the nanoscopic element stack. At least one of the nanoscopic elements is capable of switching among a plurality of electronic states in response to a corresponding electrical stimuli applied by the control circuitry to the conductive terminal and the portion of the nanoscopic element stack. For each electronic state, the nanoscopic element stack provides an electrical pathway of corresponding resistance.