A theory is developed to describe the electronic structure of mixed-valent, exchange-coupled organic biradicals. The phenomena described are analogous to those of spin-dependent delocalization observed in binuclear inorganic complexes in the sense that coupling of delocalized hole states favors a triplet state over a singlet state. However, the mathematical description of the delocalization is quite similar to Kramers' treatment of antiferromagnetic and ferromagnetic terms in metal oxides (Physica 1934, 1, 182). There is a similarity in that a delocalized orbital in the mixed-valent biradical anion can play the role of oxide in conventional superexchange. As in Kramers' theory, there are two terms that result from the analysis, a second-order term and a third-order term. However, the significance of the terms is different for delocalized magnetic orbitals than for the metal-bridge-metal system considered by Kramers. The computational chemistry shows that the third-order ferromagnetic term dominates for large dihedral angles, in agreement with previous experimental results. The mechanism presented suggests a new paradigm for the design of high-spin organic molecules.