  We discuss the Minkowski stability problem in modified gravity by using
dynamical system approach. The method to investigate dynamical stability of
Minkowski space was proposed. This method was applied for some modified gravity
theories, such as $f(R)$ gravity, $f(R)+\alpha R\Box R$ gravity and
scalar-tensor gravity models with non-minimal kinetic coupling. It was shown
that in the case of $f(R)$ gravity Minkowski solution asymptotically stable in
ghost-free ($f'>0$) and tachyon-free ($f">0$) theories in expanding Universe
with respect to isotropic and basic anisotropic perturbations. In the case of
higher order gravity with $\alpha R\Box R$ correction conditions of Minkowski
stability with respect to isotropic perturbations significantly different:
$f'(0)<0$, $f"(0)<0$ and $3f'(0)+f"(0)^2/\alpha>0$. And in the case of
scalar-tensor gravity with non-minimal kinetic coupling Minkowski solution
asymptotically stable in expanding Universe with respect to isotropic
perturbations of metric. Moreover the developed method may be used for finding
additional restrictions on parameters of different modified gravity theories.
