Cable-conduit mechanism (CCM) is widely used in robotic hands, rescue robots, rehabilitation robots, and surgical robots because it offers efficient transmission of forces/torques from the external actuator to the end effector with lightweight and high flexibility. However, the accurate position control is challenging in such mechanism due to friction and backlash-like hysteresis between the cable and the conduit. In this paper, a new control approach is proposed to enhance the trajectory tracking performances of the CCM. Unlike current approaches for the CCM in the literature, the proposed scheme considers the position transmission of the CCM as an approximation of backlash-like hysteresis nonlinearities without requiring the exact values of model parameters and their bounds. Online approximation-based robust control laws, which have the capabilities of estimating unknown system parameters, are also established. In addition, the deigned controller can adapt to any changes of the cable-conduit configuration and it is stable. The results of the proposed control techniques have been experimentally validated on a flexible robotic system using a flexible endoscope. Experimental validations show substantial improvements on the performances of position tracking for the use of CCM regardless of the arbitrary changes of the cable-conduit configurations.