In this paper, the stability and evolutionary trend of Hopf bifurcations are investigated thoroughly for the double-input SEPIC DC–DC converter with one-cycle control (OCC), which is widely used in hybrid power systems. By means of cycle-by-cycle simulations, the evolutionary trend of bifurcation behaviors is identified. The inherent mechanisms of two types of bidirectional Hopf bifurcations are uncovered based on the proposed averaged model. Moreover, stability boundaries in the parameter space are derived with the help of eigenvalue analysis to optimize the circuit design. Furthermore, some important indices with respect to coupling effects are evaluated to assess the coupling effects in the system. Finally, PSpice circuit experiments are performed to verify the bifurcation analysis.