  We consider cosmological dynamics in generalized modified gravity theory with
the $R\Box R$ term added to the action of the form $R+R^N$. Influence of $R
\Box R$ term to the known solutions of modified gravity is described. We show
that in particular case of $N=3$ these two non-Einstein terms are equally
important on power-law solutions. These solutions and their stability have been
studied using dynamical system approach. Some results for the case of $N \ne 3$
(including stability of de Sitter solution in the theory under investigation)
have been found using other methods.
