Magnetization M(T, B) of powder and glassy samples containing carbon nanoparticles, not intentionally doped and doped with Ag, Au and Co, is investigated at temperatures T between - 3-300 K in magnetic fields B up to 5T. According to atomic force microscopy data, a system of carbon particles has a broad size distribution, given by the average and the maximum radii of -60 nm and - 110 nm, respectively. In low fields of B << B(K), where B(K) - 1T is the mean anisotropy field, M(T) exhibits large irreversibility or deviation of zero-field cooled and field-cooled magnetizations, which is suppressed completely at B > B(K). The dependence of M(B) saturates above B - 2T at T - 150-300 K and contains a large paramagnetic-like response below - 50-150 K. Hysteresis is observed already at 300 K and is characterized by a power-law temperature decay of the coercive field, B(c)(T). This is described by the exponent n approximately 0.8 and by the low-temperature values of B(c) (0) increasing from -36-53 mT in the undoped sample and those doped with Ag and Au, up to 80 mT in the Co-doped material, yielding the blocking temperatures T(b) approximately 400-580 K. Analysis of the experimental magnetization data above suggests distribution of the magnetization close to the surface of the particles, yielding a thickness of the near-surface layer, h, filled with localized magnetic moments, micro1 - microB, to be close to the average distance, a, between the moments, h approximately a - 1 nm. This is consistent with the origin of magnetism in nanocarbon being presumably due to intrinsic near-surface defects.