The present paper is the first stage of our study of Martian satellite dynamics. The ERA system was used for developing the numerical dynamical theory of Phobos and Deimos. The database of the observations of different types was constructed in the form of ERA tables. At present the main features of the model are realized in the framework of the ERA system. Our results are in good agreement with those obtained by other authors. A further development of the theory (for example, inclusion of the secular acceleration) and expansion of the database of the satellites observations is assumed.