This study investigates the transient interaction behaviours in SEPIC DC-DC converters by using non-linear modal series method. Based on the derived non-linear model, the analytical approximate solutions are obtained to characterise the transient behaviours of the converters. Then, fundamental modal analysis is performed to identify the correlation among system parameters, fundamental modes and state variables so that system key parameters are subsequently acquired. In addition, the second-order interaction indices are evaluated in order that the underlying mechanism of non-linear interaction behaviours is uncovered. Finally, theoretical analysis is verified by circuit experiments. These results are beneficial to the improvement of the transient behaviours and the system reliability.