We show that ultrathin GaN membranes, with a thickness of 15 nm and planar dimensions of 12 × 184 μm(2), act as memristive devices. The memristive behavior is due to the migration of the negatively-charged deep traps, which form in the volume of the membrane during the fabrication process, towards the unoccupied surface states of the suspended membranes. The time constant of the migration process is of the order of tens of seconds and varies with the current or voltage sweep.