We study the electron spin resonance (ESR) signal of pristine and potassium doped SWCNTs. We identify signals of a superparamagnetic background, a low intensity impurity, and of the conduction electron spin resonance (CESR). The latter only appears upon the alkali atom doping. To identify the CESR signal, we critically assess whether it could come from residual graphitic carbon, which we clearly exclude. We give accurate values for the signal intensities and the corresponding concentration of spins and for the g-factors. The CESR signal intensity allows to determine the density of states on the SWCNT assembly. (C) 2009 WILEY-VCH Verlaq GmbH & Co. KGaA, Weinheim