Semiempirical MNDO and density functional theory (B3LYP/3-21G) were used to examine the relative stability of the isomers of successive BN-substituted fullerenes C60-2x(BN)(x), where x = 1-24. Doing so established certain rules of successive BN substitution in cagelike carbon materials. HOMO-LUMO gaps were also estimated for the entire series. It was found that heterofullerenes with less than 40% BN substitution have smaller band gaps than does semiconducting C-60.