Spacecraft attitude and orbit estimation are considered very important tasks for nearly every spacecraft. The full state estimation process is usually done using the Extended Kalman Filter (EKF). Nonlinearities associated with spacecraft model, measurement model, and disturbance models represent a serious obstacle for EKF to be implemented on-board a spacecraft. In order to overcome this problem, two neural networks architecture are developed. They are the direct architecture and the cross-feeding architecture. The first one can estimate the spacecraft orbital states but it has a degraded accuracy for the spacecraft representing attitude states. A modification of the direct architecture is made to enable simultaneous estimation of spacecraft attitude and orbit states and named as cross-feeding architecture. The cross-feeding architecture has outperformed the EKF. It has the same accuracy as the EKF, with less than half of its execution time. An EKF is used to provide data set for training and validation of the neural networks solution. In order to avoid overfitting and enhance network generalization, 15% of the EKF data set is used to validate the solution. The developed algorithms have the ability to deal with initial high estimation errors without using any small angle approximation. Thus, the developed algorithms can work in all the spacecraft operational modes.