NRAM arrays with nanotube blocks, traces and planes, and methods of making the same are disclosed. In some embodiments, a nanotube memory array includes a nanotube fabric layer disposed in electrical communication with first and second conductor layers. A memory operation circuit including a circuit for generating and applying a select signal on first and second conductor layers to induce a change in the resistance of the nanotube fabric layer between the first and second conductor layers is provided. At least two adjacent memory cells are formed in at least two selected cross sections of the nanotube fabric and conductor layers such that each memory cell is uniquely addressable and programmable. For each cell, a change in resistance corresponds to a change in an informational state of the memory cell. Some embodiments include bit lines, word lines, and reference lines. In some embodiments, 6F2 memory cell density is achieved.