This article is devoted to the fixed-time synchronous control for a class of uncertain flexible telerobotic systems. The presence of unknown joint flexible coupling, time-varying system uncertainties, and external disturbances makes the system different from those in the related works. First, the lumped system dynamics uncertainties and external disturbances are estimated successfully by designing a new composite adaptive neural networks (CANNs) learning law skillfully. Moreover, the fast-transient, satisfactory robustness, and high-precision position/force synchronization are also realized by design of fixed-time impedance control strategies. Furthermore, the “complexity explosion” issue triggered by traditional backstepping technology is averted efficiently via a novel fixed-time command filter and filter compensation signals. And then, sufficient conditions of system controller parameters and fixed-time stability are theoretically given by establishing the Lyapunov stability theorem. Besides, the absolute stability of the two-port networked system under complex transmission time delays is rigorously proved. Finally, simulations are performed with 2-link flexible telerobotic systems under two cases, results are presented to realistically verify the proposed control algorithm available.