We propose and evaluate first principles methods for calculating the nuclear shielding tensor in open-shell, paramagnetic molecules, dealing with the case of small spin-orbit coupling that, in turn, implies the best applicability to light, organic compounds. The formalism is consistent up to second order in the fine structure constant, and includes orbital, fully anisotropic dipolar, and isotropic contact contributions to the tensor. The proposed method is implemented within the ab initio single- and multiconfiguration self-consistent field as well as density functional theory frameworks. The applications include small main-group radicals and larger nitroxide radicals. The analysis of the results and comparison with the experimental nuclear magnetic resonance data, which are available for the latter compounds, indicate promising accuracy and applicability of the density functional theory method to chemically interesting problems. (C) 2003 American Institute of Physics.