This paper presents an approach for a derivative-free adaptive controller for two-link flexible robots within the joint space. The proposed method addresses the trajectory tracking problem in the joint space, particularly for robots with flexibility and high uncertainty in system parameters. Initially, a linearizing control approach is employed to approximately eliminate the nonlinear behavior of the robot. Subsequently, a linear static compensator is applied to stabilize the tracking error within the nominal system. To address uncertainties arising from link flexibilities and vibration modes, a derivative-free adaptive signal is utilized to approximate and eliminate their impact on tracking performance. The effectiveness of the suggested controller is verified using a two-link flexible and illustrated through computer simulations.