Presentation is given of general method of the calculus of proximity of elliptical orbits, with the eccentric anoma ies as basic variables. Equations are derived for the determination of points at the minimum mutual distance, irrespective of how great is the angle between the orbital planes. These equations being transcendent, their solution is performed by the method of successive approximations. One proceeds thereby from the approximate values of eccentric anomalies, which are fairly close to those searched for their successive corrections are being determined. The procedure is very effective and suited to the serial investigation. It is illustrated by some examples of minor planet pairs.