The stability of all 23 C58N2 and C58B2 heterofullerenes, in the singlet and triplet states was determined at the B3LYP/6-31G** level. In equilibrium mixture the achiral (1,4) C58N2 isomer would be populated in ca. 95.8%, the chiral (1,16) one in ca. 3.3%, and the achiral (1,4) C58B2 in 100%, whereas all triplet state isomers are less stable. Fourteen out of 23 C58X2 are chiral. Four different chirality measures were calculated by Our own CHIMEA program: pure geometrical, labeled, mass, and charge. Intercorrelations between the measures for all chiral compounds indicate that the pure geometrical chirality measure is unstable and should not be used in QSAR predictions of the other molecular properties, while the labeled and mass-weighted ones are promising QSAR descriptors. For each chiral C58N2 molecule, some very strong VCD bands, of intensity comparable with that in the IR spectra, can serve in identification and characterization of the isomers.