A robust neural adaptive integral sliding mode control approach is proposed in the present paper for nonlinear exoskeleton systems. The proposed control technique is composed of two parts: an adaptive neural network controller and an adaptive integral terminal sliding mode controller. The adaptive laws are developed to estimate unknown parameters and ensure asymptotic stability of the closed-loop system. Only classical system's properties are supposed to be known, such as the bounds on some parameters. The unknown dynamics of the system are estimated on line by the neural network control part. The proposed adaptive control strategy is designed to ensure the reaching of the sliding surface with enhanced tracking performance. The singularity problem of the terminal sliding mode approach is overcomed without adding any constraint. The closed-loop stability of the system in the sense of Lyapunov is demonstrated. The effectiveness of the proposed approach is tested in real time application with healthy human subjects by performing passive arm movements using a 2-DOF upper limb exoskeleton.