(en) A tight-binding hamiltonian is constructed to investigate the electronic band structure of nano-scale carbon fibers composed of two or three concentric graphene layers. The individual tubule layers have the so-called armchair, achiral geometry and are known to be metallic. After interlayer interactions are switched on, it is found that a multilayered nanofiber can become a semimetal or even a semiconductor for certain positions of the tubules relative to each other.