  In the present work we investigate the Newtonian limit of higher-derivative
gravity theories with more than four derivatives in the action, including the
non-analytic logarithmic terms resulting from one-loop quantum corrections. The
first part of the paper deals with the occurrence of curvature singularities of
the metric in the classical models. It is shown that in the case of local
theories, even though the curvature scalars of the metric are regular,
invariants involving derivatives of curvatures can still diverge. Indeed, we
prove that if the action contains $2n+6$ derivatives of the metric in both the
scalar and the spin-2 sectors, then all the curvature-derivative invariants
with at most $2n$ covariant derivatives of the curvatures are regular, while
there exist scalars with $2n+2$ derivatives that are singular. The regularity
of all these invariants can be achieved in some classes of nonlocal gravity
theories. In the second part of the paper, we show that the leading logarithmic
quantum corrections do not change the regularity of the Newtonian limit.
Finally, we also consider the infrared limit of these solutions and verify the
universality of the leading quantum correction to the potential in all the
theories investigated in the paper.
