The ground and very low-lying excited states of new Mg2C and Mg3C molecules have been studied using high-level ab initio techniques. Four structures of Mg2C, (C-2 upsilon, (1)A(1)), (C-2 upsilon, B-3(1)), (D-infinity h, (3) Sigma(g)(-)), and (D-infinity h, (5) Sigma(u)(-)), were found to lie within 4 kcal/mol (at QCISD(T)/6-311+G(2df)) of one another. A C-3 upsilon ((1)A(1)) structure was found to be the only low-energy structure for Mg3C. Both Mg2C and Mg3C were found to be thermodynamically stable with respect to all dissociation channels. Dissociation energies are found to be, for Mg2C (C-2 upsilon, (1)A(1)) --> MgC ((3) Sigma(-))+Mg (S-1), 24.6 kcal/mol and, for Mg3C (C-3 upsilon, (1)A(1)) --> Mg2C (C-2 upsilon, (1)A(1))+Mg (S-1), 41 kcal/mol at the QCISD(T)/6-311+G(2df)+ZPE level.