  We suggest two realistic f(R) and one F(G) modified gravities which are
consistent with local tests and cosmological bounds. The typical property of
such theories is the presence of the effective cosmological constant epochs in
such a way that early-time inflation and late-time cosmic acceleration are
naturally unified within single model. It is shown that classical instability
does not appear here and Newton law is respected. Some discussion of possible
anti-gravity regime appearence and related modification of the theory is done.
