  If one has to attain high accuracy over long timescales during the numerical
computation of the N-body problem, the method called Lie-integration is one of
the most effective algorithms. In this paper we present a set of recurrence
relations with which the coefficients needed by the Lie-integration of the
orbital elements related to the spatial N-body problem can be derived up to
arbitrary order. Similarly to the planar case, these formulae yields
identically zero series in the case of no perturbations. In addition, the
derivation of the formulae has two stages, analogously to the planar problem.
Namely, the formulae are obtained to the first order, and then, higher order
relations are expanded by involving directly the multilinear and fractional
properties of the Lie-operator.
