  The present paper reconsiders the Newtonian limit of models of modified
gravity including higher order terms in the scalar curvature in the
gravitational action. This was studied using the Palatini variational principle
in [Meng X. and Wang P.: Gen. Rel. Grav. {\bf 36}, 1947 (2004)] and
[Dom\'inguez A. E. and Barraco D. E.: Phys. Rev. D {\bf 70}, 043505 (2004)]
with contradicting results. Here a different approach is used, and problems in
the previous attempts are pointed out. It is shown that models with negative
powers of the scalar curvature, like the ones used to explain the present
accelerated expansion, as well as their generalization which include positive
powers, can give the correct Newtonian limit, as long as the coefficients of
these powers are reasonably small. Some consequences of the performed analysis
seem to raise doubts for the way the Newtonian limit was derived in the purely
metric approach of fourth order gravity [Dick R.: Gen. Rel. Grav. {\bf 36}, 217
(2004)]. Finally, we comment on a recent paper [Olmo G. J.: Phys. Rev. D {\bf
72}, 083505 (2005)] in which the problem of the Newtonian limit of both the
purely metric and the Palatini formalism is discussed, using the equivalent
Brans--Dicke theory, and with which our results partly disagree.
