Intensities of a1Δg[LEFTWARDS ARROW]X3g and b1g+ [LEFTWARDS ARROW] X3g transitions in molecular oxygen have been calculated on the basis of the INDO method taking into account spin-orbit coupling by perturbation theory. The transitions are magnetic dipole in nature. The first of them (aX) steals its intensity from 3Πg-3g and 1Πg-1Δg transitions, which are determined by the orbital angular-momentum operator. This source is not the principal one for the intensity of the second (b-X) transition. Its intensity is stolen principally from microwave transitions between spin sublevels of the ground 3g state. The last source explains the large difference in intensities of the a-X and b-X transitions. Calculated oscillator strengths are in a good agreement with experiment. The same integrals that determine the intensity also determine the parameters of the spin Hamiltonian for the ground 3g state. These parameters are in a good agreement with experiment also, showing the validity of the whole calculation. In a condensed phase the investigated transitions are enhanced by intermolecular exchange interaction. It is known that an external heavy atom (EHA) enhances the b-X transition of oxygen in solution, but does not influence the a-X transition. In the collision complex O2-EHA, which has a geometry without inversion symmetry, the microwave transitions between spin sublevels of the “3g” state obtain electric-dipole moments, which are stolen from the charge-transfer transition. This mechanism explains the selective effect of EHA.