A hybrid nonlinear controller for spacecraft attitude and rate tracking is presented through a combination of two control techniques. The basic control scheme is developed using a Modified State-Dependent Riccati Equation MSDRE based on a pseudo-linear formulation of spacecraft augmented dynamics and kinematics. A neuro-fuzzy controller is designed using an Adaptive Neuro-Fuzzy Inference System ANFIS utilizing the off-line solutions of the MSDRE. The combined control scheme is applied according to large time intervals of the MSDRE solutions to obtain the optimal control torques while along each time interval the ANFIS controller provides the required control signal. The global asymptotic stability of the MSDRE and MSDRE/ANFIS is investigated using Lyapunov theorem. The results show a considerable amount of reduction in the computational burden while the tracking accuracy is dependent on the size of the time interval to update the ANFIS controller.