The reaction mechanisms for NCX (X = O, S) with C2H2 was studied theoretically. The possible reaction mechanisms of NCO + C2H2 investigated in this study were categorized into five different pathways leading to the five possible final products: HCCO + HCN, HNCO + HNC, HNCO + C2H, HONC + C2H, and HC2NCO + H, labeled in order from P1 to P5, respectively. Similar calculations were also carried out for the NCS counterpart, and the energy barriers as well as the products were compared. Direct hydrogen abstraction is favored in the formation of HNCO instead of HOCN. In contrast, it is much easier to form HSCN rather than HNCS. There are two different paths for the oxazole/thiazole formation as an intermediate, and the order of energy barriers of these two paths is opposite in NCO and NCS. The product channel of HNCO/HSCN + C2H may be kinetically favored at higher temperature. Other product channels are consistent with the experimental prediction of the formation of initial short-lifetime NCO/NCS-CH2 adducts which then undergo rapid transformation into the products.