The procession of a satellite stabilized by rotation is investigated in the presence of nonzero-valued initial conditions with respect to the angle and angular velocity, as well as perturbing torques. A dynamically asymmetrical satellite whose structural axes do not coincide with the principal central inertial axes is considered. Conditions are formulated such that the precession of the satellite is small. Approximate solutions are given for the dynamic and kinematic equations, along with formulas for estimating the deviation of the rotational axis of the satellite from a prescribed direction.