  Dynamical systems methods are used to study the evolution of the Bianchi I
model with a scalar field. We show that inclusion of the non-minimal coupling
term between the scalar field and the curvature changes evolution of the model
compared with the minimally coupled case. In the model with the non-minimally
coupled scalar field there is a new type of singularity dominated by the
non-minimal coupling term. We examine the impact of the non-minimal coupling on
the anisotropy evolution and demonstrate the existence of its minimal value in
the generic case.
