An anode for a rechargeable lithium cell comprises carbon nanotubes that contain within them an element that can form alloys or compounds reversibly with lithium over a range of compositions. The element within the nanotubes may be aluminum or tin. These carbon nanotubes are bound together to form a coherent layer with a polymeric binder, such as a polymer of viniylidene fluoride. A cell with such an anode should have improved capacity and improved reversibility, because the nanotubes provide a stabilizing framework for the alloy.