Hybrid functional electrical stimulation (FES) cycling is a method to rehabilitate people with neurological conditions when they are not in and of themselves capable of fully controlling their extremities. To ensure smooth cycling and adequate stimulation to accomplish the rehabilitation task, admittance control is applied between the human and the robotic cycle. The cycle motor is actuated by a dual neural network control structure with an additional robust element tracking the admittance trajectory, while muscles are stimulated with a simple saturated robust controller. The dual neural network structure allows adaptation to separable functions of the dynamic system, in addition to shared adaptation through the admittance filter. A Lyapunov analysis shows that the admittance tracking controller is globally exponentially stable. A passivity analysis shows that the admittance system and cadence tracking error are output strictly passive. A combined analysis shows that the total system is passive. Experiments are performed on eight participants without neurological conditions, on 12 differing protocols including a robust controller for comparison, the addition of noise, and the addition or lack of stimulation. One participant with a neurological condition was evaluated on three different protocols, including a robust controller, a neural network controller, and a game-like mode where the participant was asked to track the trajectory as it appeared on a screen. Statistical analysis of the experiments show that the standard deviation of the tracking error is significantly improved with the adaptive dual neural network control addition when compared to the robust controller, in some instances reducing the magnitude by half.