This article contains two systems of formulas for the determination of the long-period perturbations caused by the sun and the moon in the motion of an artificial satellite. The first system can be used for the determination of the lunar effect for all satellites. The second method is more convenient for finding the lunar effect for close satellites and the solar effect for all satellites. The knowledge of these effects is essential for the determination of the stability of the orbit of the satellite. The basic equations of both systems are arranged in a form that permits the use of numerical integration. The two theories are more accurate and more adaptable to the use of electronic machines than are the analytical developments obtained previously.