The possible existence of complexes formed by the C60 fullerene or its derivatives with transition metals interacting with the carbon cage via η6−π type bonding is discussed. The derivatives C60R6 of the C60 fullerene (R = −, H, F, Cl, Br, CN) are analyzed using the density functional method within the Perdew-Burke-Ernzerhof approximation. In these molecules, the R groups are attached to carbon atoms located in the α positions with respect to the common hexagon of the C60 fullerene. The structure and electron configuration of complexes formed by these molecules with Cr(C6H6), Cr(CO)3, MoC6H6, and Mo(CO)3 particles are modeled. The “dimer” systems C60R6-M-R6C60 (M = Cr, Mo, R =-, H, F) are investigated in which two fullerene molecules interact via a transition-metal atom. It is found that the introduction of six R groups in the α sites with respect to the common hexagon of C60 favors the formation of complexes of these derivatives of the C60 fullerene with the Cr(C6H6), Cr(CO), Mo(C6H6), and Mo(CO)3 particles in which η6-π type bonds arise between the metal and the atoms of the hexagon fringed with the R groups. It is also demonstrated that analogous complexes with a “bare” C60 fullerene are possible, but they are significantly less stable. The (C6H6) M-R6C60R6-M (C6H6) complexes of particles M(C6H6) (M= Cr, Mo) and derivatives R6C60R6 (R =-, H, F, Cl, Br) are studied. In the R6C60R6 molecule, six R groups are located in the α sites with respect to the common hexagon of the C60 fullerene and six other groups fringe the opposite hexagon. The obtained results can be applied to planning synthesis of new complexes that C60 fullerene derivatives can form with transition metals.