Using the density functional theory, we investigated the possible formation of fullerene-dizincocene hybrids, specifically C(60)*-Zn-Zn-Cp*, C(60)*-Zn-Zn-C(60)*, C(70)*-Zn-Zn-Cp*, and C(70)*-Zn-Zn-C(70)*, where C(60)*, Cp*, and C(70)* represent C(60)(CH(3))(5), C(5)(CH(3))(5), and C(70)(CH(3))(5) radicals. Our calculation shows that these hybrids have HOMO-LUMO gaps which are larger than has been experimentally identified for C(60)*-Fe-Cp. In addition, the strength of the Zn--Zn bonds is similar to that in Cp*-Zn-Zn-Cp* which was also synthesized recently. Furthermore, heterohybrids, C(60)*-Zn-Zn-Cp* and C(70)*-Zn-Zn-Cp* are expected to exist in equilibria with homohybrids, C(60)*-Zn-Zn-C(60)* and C(70)*-Zn-Zn-C(70)*, in which heterohybrids are much more favored. On the other hand, another hybrid involving Sc(3)N@C(68) as a fullerene unit is not highly probable.