  We discuss possible instabilities in higher-derivative matter fields
theories. These theories has two free parameters $\beta_1$ and $\beta_4$. By
using dynamical system approach we explicitly demonstrate that for stability of
Minkowski space in expanding Universe it is need condition $\beta_4<0$. By
using quantum field theory approach we also find additional restriction for
parameters $\beta_1>-\frac{1}{3}\beta_4$ which is need to avoid tachyon-like
instability.
