The long‐range (secular) effects caused by the moon and the sun are of primary importance for establishing the stability of highly eccentric orbits of satellites. At present no complete analytical theory exists that can treat such orbits. In this paper Halphen's method of treating secular planetary effects is suggested also for the determination of long‐range lunar effects in the motion of artificial satellites, using step‐by‐step integration. Halphen's method permits the numerical integration of long‐range lunar effects over an interval of many years. The long‐range solar effects can be treated by averaging the disturbing function over the orbit of the satellite. Halphen's method is applicable to the determination of long‐range effects in the motion of minor planets over the interval of hundreds of thousands of years. We assume that no sharp commensurability between mean motions of the disturbed and disturbing bodies exists. A complete theory of Halphen's method is presented, using modern symbolics. Goursat transformations and a summability process are applied to speed up the convergence of series appearing