The problem of motion of a zero-mass point P in a gravitational field of free mass points is considered. The required accuracy for taking into account the perturbing acceleration of the point P is given. The "inner" (the perturbing body is closer to the attracting center than the perturbed body) and general (arbitrary location of the bodies) cases are considered. The admissible error in representing the motion of perturbing bodies is estimated. The limiting cases are considered. Examples of estimations of the required accuracy of the theory of motion of perturbing bodies are given for Earth's artificial satellites and Solar System bodies. © 1998 MAEe Cyrillic signK Hayκa/Interperiodica Publishing.