The electron-spin g shifts (magnetic moments mu (S)) of X(2)Sigma (+)(1 pi (4)3 sigma) radicals MX(+/-) with nine valence electrons are calculated at their equilibrium geometries, using second-order perturbation theory, a Hamiltonian based on Breit-Pauli theory, and correlated (MRCI) wave functions. Eighteen diatomics have been studied: BeF, BeO-, BeCl,MgF, MgO-, and MgCl (class I); BF+, BCl+, AlF+, and AlCl+ (class II); and BO, BN-, BS, BP-, AlO, AlN-, AlS, and AlP- (class III). Most radicals have small Deltag(parallel to) values (approximate to -100 ppm) and large negative agi values (-800 to -8500 ppm), except for AlN- and AlP-, which have positive agi values (1400 and 10 000 ppm) due to the quasi-degeneracy X(2)Sigma (+)/1(2)Pi (i). The sum-over-states expansions for Deltag(perpendicular to) are dominated in classes I and II by the coupling with 1(2)Pi (r), and in class III with both 1(2)Pi (i) and 2(2)Pi (r). The (2)Pi (r)(3 sigma -->2 pi) state always contributes negatively, whereas (2)Pi (i)(1 pi -->3 sigma) contributes positively for most radicals but negatively for the boron series BO, BN-, BS, and BP-. Experimental g shifts, which are available for eight of the radicals studied here, are generally well reproduced by the Deltag values calculated at R,. However, for radicals having a very low-lying 1(2)Pi (i) state, such as AlN- and AlP-, our study suggests that future calculations should include vibrational averaging to describe the (unknown) experimental data correctly. Theoretical and experimental g(perpendicular to) shifts are compared with those estimated from spin-rotation coupling constants gamma, via Curl's equation.