We theoretically study the magnetoresistance of single wall carbon nanotubes (SWCNTs) in the ballistic transport regime, using a standard tight-binding approach. The main attention is directed to spin-polarized electrical transport in the presence of either axial or perpendicular magnetic field. The method takes into account both Zeeman splitting as well as size and chirality effects. These factors ( along with a broadening of energy levels due to a strong nanotube/electrode coupling) lead, in ultra small SWCNTs, to serious modi. cations in pro. le of the Aharonov-Bohm oscillations. Other noteworthy findings are that in the parallel configuration ( axial magnetic field) the ballistic magnetoconductance is negative ( positive) for armchair (semiconducting zigzag) nanotubes, whereas in the perpendicular configuration the magnetoresistance is nearly zero both for armchair and zigzag SWCNTs. (c) 2006 Elsevier B.V. All rights reserved.