The rate constants for the reactions of C-2(X-1 Sigma(+)(g)) with H-2 and D-2 have been investigated experimentally and theoretically to assess the statistical theory of the reaction and to reveal the mechanism of the reaction. The ground-state C-2 radicals were generated by multiphoton laser-photolysis of C2Cl4 at 248 nm and were probed by a laser-induced fluorescence method using the Mulliken system (D-1 Sigma(+)(u)-X-1 Sigma(+)(g)). Rate constants have been measured to be k[C-2(X)+H-2] = 5.6 x 10(-11) exp[-9.1 (kJ mol(-1))/RT] and k[C-2(X)+D-2] = 3.2 x 10(-11) exp[-9.9 (kJ mol(-1))/RT] cm(3) molecule(-1) s(-1) in the temperature range 293-395 K and at total pressure around 10 Torr (He buffer). Quantum chemical calculations at the MRCI level revealed that the reaction predominantly proceeds via a collinear direct-abstraction transition state. The measured rate constants as well as the kinetic isotope effect were well reproduced by the transition-state theory based oil the MRCISD+Q/aug-cc-pV5Z calculations, provided that the anharmonic bending vibrations of the transition states were properly treated. The effect of the Davidson correction was found to be significant for the potential energy surface around the early transition state.