  The modified gravity with $\ln R$ or $R^{-n} (\ln R)^m$ terms which grow at
small curvature is discussed. It is shown that such a model which has
well-defined newtonian limit may eliminate the need for dark energy and may
provide the current cosmic acceleration. It is demonstrated that $R^2$ terms
are important not only for early time inflation but also to avoid the
instabilities and the linear growth of the gravitational force. It is very
interesting that the condition of no linear growth for gravitational force
coincides with the one for scalar mass in the equivalent scalar-tensor theory
to be very large. Thus, modified gravity with $R^2$ term seems to be viable
classical theory.
