  A simple example is given of the implementation of the usual method of
asymptotic expansions for weak gravitational fields. A scalar, preferred-frame
theory of gravitation is considered, but the method is general. Two kinds of
asymptotic expansion are a priori possible: "post-Newtonian" (PN) or
"post-Minkowskian", the latter allowing to account directly for propagation
effects. However, it is shown that only the PN asymptotic expansion is
compatible with the Newtonian limit. It is also shown that, in the scalar
theory, there is no non-Newtonian effect (in particular, no propagation effect)
up to the second order, i.e., the order 1/c^2.
