Secondary arcs are a type of alternating-current electric arc burning in open space, the arcing times of which are closely related to the transient of their currents. To elucidate the formation mechanism of the transient, the secondary current was first decomposed into the natural component and the forced component. Then, the corresponding circuit models were established and the formulas calculating these two components were derived. By means of the electromagnetic transients program simulation, the typical secondary arc current waveform is gotten, and its evolution is divided into three stages based on its characteristics. The influences of key factors (e.g., secondary arc resistance, shunt compensation degree, and neutral reactor) on the transient were investigated, and the most critical factor was obtained. It indicates that the transient of secondary arc current is mainly characterized by its natural component. Furthermore, using the Laplace transform method, and along with the simplification of the system circuit, the characteristic equation for the UHV transmission line was developed, and the damping factors and resonant frequencies of the natural component were solved. Compared with the previous steady-state analysis, the relationship between the decaying and oscillating processes with the system parameters is quantitatively explained. Rather than the line length, the neutral reactor, the decay of secondary arc current is directly proportional to the arc resistance, but inversely proportional to shunt reactor. The proposed methodology can be also applied to recovery voltage study. The results are essential for the transient analysis, the choice of neutral reactor, as well as the implementation of single-phase auto-reclosing strategy.