Density functional calculations including nonlocal corrections to the exchange and correlation energies have been carried out on mono-and bimetallic metallocarbohedrenes (met-cars) of titanium and zirconium Ti-x-ZryC12 (y = 0, 1, 3, 4, 5, 8; x + y = 8), as well as on the endohedral and exohedral conformations of Ti8C13 and on Ti7C12. For all considered molecules, geometry optimizations have been carried out assuming for the. metal framework the structure of tetracapped tetrahedron with two distinct sets of metal sites which has been consistently computed to be the most stable one for Ti8C12 and related species. For mixed-metal met-cars, zirconium atoms have been assigned to occupy either sites of the capped tetrahedron br sites of the capping tetrahedron, thus generating two conformers for each value of y different from 0 or 8. The total energies of those pairs of conformers have been found to differ by less than 1.5 kcal mol(-1) for all considered bimetallic stoichiometries. This similar behavior of the two sets of metallic sites regarding the single or multiple substitution of Ti by Zr could explain the regular distribution of the peaks in the mass spectra of TixZryC12 (y = 0-5), which had been interpreted up to now as providing evidence that the eight metal atoms were actually equivalent. At variance from metal substitution, metal dissociation is found very sensitive to the site to which the removed atom belongs. The present study confirms that the structure of tetracapped tetrahedron assumed for Ti8C12 is extremely favorable to the encapsulation of an extra carbon atom. Exohedral conformations are less' stable due to the presence of two unpaired electrons on the extra carbon. The computed electron affinity (1.26 eV) and ionization potential (4.6 eV) of Ti8C12 are in agreement with values or estimates recently reported from experiment. It finally appears that none of the properties of Ti8C12 and other met-cars reported to date are in contradiction with the assumption of a tetrahedral structure with two distinct sets of metal sites.