The stability of strongly bound excited states of C2, C+ 2 and C2+ 2 resulting from double excitations of the type σ2 u→ MO2 relative to the ground-state configuration (with MO2 standing for 3σ2 g,3σg1πu or 1π2 u) was investigated using a multi-reference MRD-CI method. For C2, the doubly excited configuration 3σ2 g1π4 u, corresponds to the experimentally observed E1Σ+ g (31Σ+ g) state, which exhibits a heavy mixing with the less bonding configurations 2σ2 u,1π4 u (X1Σ+ g) and 2σ2 u3σ2 g1π2 u(21Σ+ g). This mixing is reflected in two ways: the E+ g state does not show the features expected for a strongly bound state (i.e. short Re and high ωe), but - despite its mainly two-electron 3σg1πu→2σ2 u character - it allows the emission band E1Σ+ g →A1Πu to be observed with a moderate intensity by one-photon spectroscopy. The states 12Σ+ u (2σulπ4 u) and 22Σ+ g (3σg1π4 u) of C+ 2 as well as 23,1Πu (3σg1π3 u) and 31Σg + (1π+ u) of C2+ 2 exhibit a definite enhanced bond strength relative to the ground state. Radiative decay from all these doubly excited states into lower-lying, singly excited 2σu states should be suitable for experimental study because of favorable Franck-Condon envelopes and the one-electron character of the transition.