Ab initio CCSD(T)/cc-pVTZ(CBS)//B3LYP/6-311G** calculations of the C(6)H(7) potential energy surface are combined with RRKM calculations of reaction rate constants and product branching ratios to investigate the mechanism and product distribution in the C(2)H + 1-butyne/2-butyne reactions. 2-Ethynyl-1,3-butadiene (C(6)H(6)) + H and ethynylallene (C(5)H(4)) + CH(3) are predicted to be the major products of the C(2)H + 1-butyne reaction. The reaction is initiated by barrierless ethynyl additions to the acetylenic C atoms in 1-butyne and the product branching ratios depend on collision energy and the direction of the initial C(2)H attack. The 2-ethynyl-1,3-butadiene + H products are favored by the central C(2)H addition to 1-butyne, whereas ethynylallene + CH(3) are preferred for the terminal C(2)H addition. A relatively minor product favored at higher collision energies is diacetylene + C(2)H(5). Three other acyclic C(6)H(6) isomers, including 1,3-hexadiene-5-yne, 3,4-hexadiene-1-yne, and 1,3-hexadiyne, can be formed as less important products, but the production of the cyclic C(6)H(6) species, fulvene, and dimethylenecyclobut-1-ene (DMCB), is predicted to be negligible. The qualitative disagreement with the recently measured experimental product distribution of C(6)H(6) isomers is attributed to a possible role of the secondary 2-ethynyl-1,3-butadiene + H reaction, which may generate fulvene as a significant product. Also, the photoionization energy curve assigned to DMCB in experiment may originate from vibrationally excited 2-ethynyl-1,3-butadiene molecules. For the C(2)H + 2-butyne reaction, the calculations predict the C(5)H(4) isomer methyldiacetylene + CH(3) to be the dominant product, whereas very minor products include the C(6)H(6) isomers 1,1-ethynylmethylallene and 2-ethynyl-1,3-butadiene.