Ab initio molecular orbital calculations have been performed on the interstellar molecules C3H2 and C3H, and the reaction pathway including them for the neutral-neutral reactions C(P-3)+C2H2 in interstellar clouds were examined. The optimized structures, rotational constants, dipole moments, vibrational frequencies, IR intensities, and relative energies for the various isomers of the C3H2 and C3H species were calculated and discussed. It was found that the cyclic and linear C3H species have, respectively, two forms, and that the cyclic-C3H is more stable than the linear-C3H. New pathways for the neutral-neutral reaction C(P-3)+C2H2 along which the C3H2 species (cyclopropenylidene, propenediylidene, and propargylene) are involved were found, and, especially, the formation of the cyclic-C3H via the neutral-neutral reaction process C(P-3)+C2H2-->C3H+H passing through the cyclic-C3H2 was discovered. On the other hand, it was found that the formation of the linear-C3H cannot be explained by the mechanism via the neutral-neutral reaction.