  We consider class of modified $f(R)$ gravities with the effective
cosmological constant epoch at the early and late universe. Such models pass
most of solar system tests as well they satisfy to cosmological bounds. Despite
their very attractive properties, it is shown that one realistic class of such
models may lead to significant Newton law corrections which become small at the
future universe only. The model with acceptable Newton law regime shows the
matter instability. This suggests that more complicated version of such theory
(or extended parameters space) should be investigated.
