A partly radical character of fullerene molecules is revealed by the presence of effectively unpaired electrons (the same circumstance determines the singlet instability of solutions to the Hartree-Fock RHF and UHF SCF equations). We analyzed the instability of Hartree-Fock solutions, found the stable pure spin singlet state, and determined its energy and the properties of its wave function. Both the energy and wave function of the UHF solution were shown to closely approximate those of the stable solution. We determined the total number of effectively unpaired electrons (ND) and the partial contributions to this number of each atom (NDA) using the UHF solution. The procedure for calculations and reliability of the results obtained are discussed for the example of several diatomic molecules. The N D and NDA values were calculated for the singlet state of the X60 (X = C, Si) and C70 molecules. Independent calculations showed that the distributions of the NDA values and free valence over fullerene atoms were closely similar. This allows N DA to be used as an indicator of the chemical activity of the atoms. Copyright © 2005 by Pleiades Publishing, Inc.