  The method of asymptotic expansions is used to build an approximation scheme
relevant to celestial mechanics in relativistic theories of gravitation. A
scalar theory is considered, both as a simple example and for its own sake.
This theory is summarized, then the relevant boundary problem is seen to be the
full initial-value problem. It is shown that, with any given system of
gravitating bodies, one may associate a one-parameter family of similar
systems, the parameter measuring the gravitational field-strength. After a
specific change of units, the derivation of asymptotic expansions becomes
straightforward. Two hypotheses could be made as to which time variable has to
be used in the expansion. The first one leads to an "asymptotic" post-Newtonian
approximation (PNA) with instantaneous propagation, differing from the standard
PNA in that, in the asymptotic PNA, all fields are expanded. The second
hypothese could lead to an "asymptotic" post-Minkowskian approximation (PMA)
allowing to describe propagation effects, but it is not compatible with the
Newtonian limit. It is shown that the standard PNA is not compatible with the
application of the usual method of asymptotic expansions as envisaged here.
