We present an output-feedback control design of a two-link, flexible-joint manipulator. The control system is a combination of the Luenberger-type observer, backstepping control, variable structure control, and high-order differential neural network. Using the neural network as model identifier, we can control this complicated system without using its closed-form mathematical model. The observer provides us with the ability to design the control system from the output signals. The variable structure controller handles uncertainties arising from model identification and state estimation. Backstepping structure provides a way of applying the robust control to each subsystem. Simulation of the two-link flexible-joint manipulator is included.