This paper concentrates on the control of hybrid fuel-cell (FC)/energy-storage distributed generation (DG) systems under voltage sag in distribution systems. The proposed control strategy-makes hybrid DG system work properly when a voltage disturbance occurs in distribution system, and it stays connected to the main grid. To distribute the power between dc power sources and stabilize the dc-link power, a Lyapunov-based neuro-fuzzy control strategy has been developed. This controller determines the super-capacitor power that should be generated according to the amount of available energy in dc-link. Also, current control strategies for the FC converter (boost) and supercapacitor converter (buck-boost converter) are designed by proportional-integral and sliding-mode control consequently. Moreover, a complementary control strategy for voltage source converter based on positive and negative symmetrical components is presented to investigate the voltage sag ride-through and voltage control capability. The hybrid system is studied under unbalance voltage sag condition. Simulation results are given to show the overall system performance including active power control and voltage sag ride-through capability of the hybrid DG system.