The electron-spin magnetic moments of the superoxides LiO2 and NaO2, as parametrized by the g factors, are studied at the uncorrelated (ROHF) and correlated (MRCI) ab initio levels. The present method, which uses a perturbative approach complete to second order, is based on the Breit- Pauli Hamiltonian. In the standard C-2v notation for the MO2 radicals, Delta g(yy) > Delta g(zz) >> \Delta g(xx)\, where Delta g(aa) = g(aa) - g(e). The perpendicular component Delta g(xx), which is small and negative, is dictated by first-order terms (ground-state expectation values). The in-plane components Delta g(yy) and Delta g(zz) are large and positive. Delta g(yy) is governed by the second-order magnetic coupling between X(2)A(2) and 1(2)B(2) (electron excitation from the highest b(2) MO into the alpha(2)(pi*) SOMO), and Delta g(xx), by the coupling with two (2)A(1) states (excitations from the two highest a(1) MOs into pi*). The calculated data reproduce the experimental trends reasonable well. For the ground state X(2)A(2), the MRCI results for Delta g(xx), Delta g(yy), Delta g(zz) (in ppm, with ppm = 10(-6)) are -373 (-350), 56 800 (56 250), 7273 (6600) for LiO2; and -393 (150), 110 492 (108 600), 6868 (4600) for NaO2, with the experimental results given in parentheses (average from Ar and Kr matrices). For comparison purposes, the g shifts of the low-lying excited state 1(2)B(2) of LiO2 and NaO2, as well as the magnetic coupling parameters for O-2(-), LiO, and NaO, are also reported.