The electronic mechanisms of 1,3-dipolar cycloaddition reactions of fulminic acid (ONCH) and diazomethane (NNCH2) with HCdropCH, NdropCH, and PdropCH are studied using ab initio molecular orbital methods. The reaction mechanisms can be classified into two classes: ionic electrocyclic and diradical coupling mechanism;. Ionic electrocyclic mechanism occurs in reaction systems with a large difference in electronegativities between the two atoms of the dipolarophile and their atoms react with the atoms with each opposite charge of a 1,3-dipole. Diradical coupling mechanism occurs through two processes: the first process is a one-electron movement from the edge atom to the center atom of a 1,3-dipole, which leads to a biradical state (for ONCH, the one-electron movement occurs from the oxygen to the nitrogen atom; for NNCH2, the movement occurs from the carbon to the center nitrogen atom). The second process is the breaking of the pi-bond of the dipolarophile, which is strongly associated with the activation energy, followed by the formation of the new sigma-bond (cyclic reaction) through concerted or stepwise inodes.