Different types of multi-walled carbon nanotubes obtained by catalytic decomposition of acetylene or pyrolysis of propylene on an alumina template have been investigated for lithium storage in aprotic medium. The samples presented a high reversible storage capacity of lithium, ranging from 350 mAh/g to 780 mAh/g, depending on their physico-chemical characteristics. It has been found that the mesoporous character of the nanotubes is responsible for an important overvoltage between insertion and extraction of lithium. Especially swelling mesopores, created by the entanglement of flexible nanotubes, facilitate charging of an electrical double layer. This contributes to the important reversible capacity observed in the range from 1 V to 3 V vs Li (up to 580 mAh/g). On the other hand, solvated lithium cations easily penetrate the mesopores and the solvent molecules are decomposed at the carbon surface forming the solid electrolyte interphase (SEI). That is at the origin of the important irreversible capacity ranging from 570 mAh/g to 1080 mAh/g. Due to their pseudo-capacitance properties, these nanotubes are very promising as electrode materials of electrochemical capacitors.