Flexibility at the joint of a manipulator is an intrinsic property. Even “rigid-joint” robots, in fact, possess a certain amount of flexibility. Previous experiments confirmed that joint flexibility should be explicitly included in the model when designing a high-performance controller for a manipulator because the flexibility, if not dealt with, can excite system natural frequencies and cause severe damage. However, control design for a flexible-joint robot manipulator is still an open problem. Besides being described by a complicated system model for which the passivity property does not hold, the manipulator is also underactuated, that is, the control input does not drive the link directly, but through the flexible dynamics. Our work offers another possible solution to this open problem. We use three-layer neural networks to represent the system model. Their weights are adapted in real time and from scratch, which means we do not need the mathematical model of the robot in our control algorithm. All uncertainties are handled by variable-structure control. Backstepping structure allows input efforts to be applied to each subsystem where they are needed. Control laws to adjust all adjustable parameters are devised using Lyapunov’s second method to ensure that error trajectories are globally uniformly ultimately bounded. We present two state-feedback schemes: first, when neural networks are used to represent the unknown plant, and second, when neural networks are used to represent the unknown parts of the control laws. In the former case, we also design an observer to enable us to design a control law using only output signals—the link positions. We use simulations to compare our algorithms with some other well-known techniques. We use experiments to demonstrate the practicality of our algorithms.