The second-order DFT approach of Schreckenbach and Ziegler to the computation of EPR g tensors of doublet radicals (J. Phys. Chem. A 1997, 101, 3388), has been generalized to arbitrary spatially nondegenerate electronic states. The new technique is applied to a large number (47) of diatomic main-group radicals, in (n)Sigma (n > 2) ground states. Calculated principal components, of the EPR g tensors, are in a good agreement with experiment for main group radicals, with the average errors approaching the accuracy available in experimental matrix isolation studies (VWN average absolute error: 3.8 ppt). The agreement with experiment deteriorates for the mixed, main group-transition metal radicals (VWN error: 8.1 ppt) but the major trends in Deltag(perpendicular to) values are still reproduced. The approach largely breaks down for radicals containing chemical bonds between two transition metal atoms (VWN error: 30 ppt). In all cases, the calculated g tensors are insensitive to the choice of the approximate exchange-correlation functional, with the simple VWN LDA, and gradient-corrected BP86 and RPBE functionals, giving essentially identical results. As an example of the possible future applications of the technique, we examine the g-tensor of the first B-3(u) excited state of the trans(CNSSS)(2)(2+) cation. Our calculations for this systems agree well with the experimental results, both for the magnitudes, and for the orientations of the principal components.