The electronic structure of X60 molecules (X=C, Si) is considered in terms of 60 odd electrons and the spin-dependent interaction between them. The conditions for the electrons to be excluded from the covalent pairing are discussed. A computational spin-polarized quantum-chemical scheme is suggested to evaluate four parameters (energy of radicalization, exchange integral, atom spin density, and squared spin) to characterize the effect quantitatively. A polyradical character of the species, weak for C60 and strong for Si60, is established. © 2004 Wiley Periodicals, Inc.