  Persistent currents driven by a static magnetic flux parallel to the carbon
nanotube axis are investigated. Owing to the hexagonal symmetry of graphene the
Fermi contour expected for a 2D-lattice reduces to two points. However the
electron or hole doping shifts the Fermi energy upwards or downwards and as a
result, the shape of the Fermi surface changes. Such a hole doping leading to
the Fermi level shift of (more or less) 1eV has been recently observed
experimentally. In this paper we show that the shift of the Fermi energy
changes dramatically the persistent currents and discuss the electronic
structure and possible currents for zigzag as well as armchair nanotubes.
