In this paper, an Adaptive Radial Basis Function Artificial Neural Network (ARBFANN) control for Two-Flexible-Link Robots (TFLR) is presented. Flexible links are modeled as Bernoulli beams. The Assumed Mode Method (AMM) in conjunction with the Lagrange equation is used to derive the closed-form dynamic. Two modes are considered for each link. Singular perturbation technique is used to separate the TFLR into a fast subsystem and a slow subsystem. A stable robust two-time scale controller without any data for modeling is developed. The slow subsystem is controlled by an ARBFANN based on global approximation while the Linear Quadratic Regulator (LQR) controller stabilizes the fast subsystem. The ARBFANN with a sliding mode robust term is trained on-line to approximate unknown nonlinear system dynamics, suppress errors in the modeling of neural network and, guarantee closed-loop stability. The LQR controller is used to stabilize the fast subsystem by reducing the deviation in the state trajectory. Simulation results are included to validate the effectiveness of the proposed control strategy.