In this paper, a fault-tolerant synchronization control (FTSC) algorithm is proposed to deal with the position tracking control problem for a dual redundant hydraulic actuation system (DRHAS) working on active/active (A/A) mode and suffering from internal leakage faults, large disturbances, and force fighting between actuators. Specifically, two reference trajectories are introduced and a novel nonlinear model for the DRHAS is developed to facilitate the synthesis of position tracking control and force synchronization control. Then, a nonlinear FTSC algorithm is proposed by incorporating adaptive control and disturbance rejection control into the backstepping design. In which, a simple reconfiguration mechanism based on faulty parameters online adaptation is adopted to accommodate the faults. The matched and unmatched disturbances in both actuators are estimated by constructing four extended state observers (ESOs) and are compensated in a feedforward way. The stability analysis indicates that the proposed control algorithm can ensure prescribed tracking performance for the system under internal leakage faults and time-varying disturbances, and can make the tracking error of the faulty system converge to zero asymptotically under constant disturbances. Finally, the effectiveness of the proposed control algorithm is verified through comparative simulations.