We study field-effect transistors made of single- and double-walled carbon nanotube networks for applications as memory devices. The transfer characteristics of the transistors exhibit a reproducible hysteresis which enables their use as nano-sized memory cells with operations faster than 10 ms, endurance longer than 10(+4) cycles and charge retention of a few hours in air. We propose water enhanced charge trapping at the SiO(2)/air interface close to the nanotubes as the dominant mechanism for charge storage. We show that charge storage can be improved by limiting exposure of the device to air.