  Recently, a strong debate has been pursued about the Newtonian limit (i.e.
small velocity and weak field) of fourth order gravity models. According to
some authors, the Newtonian limit of $f(R)$-gravity is equivalent to the one of
Brans-Dicke gravity with $\omega_{BD} = 0$, so that the PPN parameters of these
models turn out to be ill defined. In this paper, we carefully discuss this
point considering that fourth order gravity models are dynamically equivalent
to the O'Hanlon Lagrangian. This is a special case of scalar-tensor gravity
characterized only by self-interaction potential and that, in the Newtonian
limit, this implies a non-standard behavior that cannot be compared with the
usual PPN limit of General Relativity.
  The result turns out to be completely different from the one of Brans-Dicke
theory and in particular suggests that it is misleading to consider the PPN
parameters of this theory with $\omega_{BD} = 0$ in order to characterize the
homologous quantities of $f(R)$-gravity. Finally the solutions at Newtonian
level, obtained in the Jordan frame for a $f(R)$-gravity, reinterpreted as a
scalar-tensor theory, are linked to those in the Einstein frame.
