Radiative lifetimes of the vibrational levels upsilon=2 to upsilon=4 of the X (2)Sigma(g)(+) ground state of the C-2(-) molecular ion have been experimentally investigated by photodetachment in a storage ring. The lifetime Df the upsilon = 3 level was 0.32+/-0.02 s for (CC-)-C-12-C-12, and 0.22+/-0.02 s for (CC-)-C-12-C-13. For both ions, the lower limit for the upsilon = 2 lifetime was 5 s, and the upper limit for the upsilon = 4 level was similar to 100 ms. The measured lifetime for u = 3 of (CC-)-C-12-C-12 is a factor of 4 smaller than found in a calculation [P. Rosmus and H. Werner, J. Chem. Phys. 80, 5085 (1984)]. The results point to the existence of at least one bound vibrational level of the lowest (4)Sigma(u)(+) state.