This paper presents the motion theories of the main satellites of Mars (Phobos, Deimos), Jupiter (Io, Europa, Ganymede, Callisto), Saturn (Mimas, Enceladus, Tethys, Dione, Rhea, Titan, Hyperion, Iapetus), and Uranus (Ariel, Umbriel, Titania, Oberon, Miranda) as constructed by numerical integration within the framework of the program package ERA (Ephemeris Research in Astronomy). The dynamical models include the mutual perturbations of the satellites, disturbances of the Sun, major planets and oblateness of the central planet (J₂, J₄). For the Phobos motion, the tidal perturbations from Mars are taken into account. The initial values of the coordinates and velocities were using the astrometric observations of different types. In addition, several improved parameters (the planet mass, J₂ and pole coordinates, the masses of the satellites) were improved for some satellite systems. The residuals, rms and comparison of our results with those obtained by other authors are given.