  We investigate the dynamics of Einstein equations in the vicinity of the two
recently described types of singularity of anisotropic and homogeneous
cosmological models described by the action $$ S=\int d^4x \sqrt{-g}{F(\phi)R -
\partial_a\phi\partial^a\phi -2V(\phi)}, $$ with general $F(\phi)$ and
$V(\phi)$. The dynamical nature of each singularity is elucidated, and we show
that both are, in general, dynamically unavoidable, reinforcing the unstable
character of previous isotropic and homogeneous cosmological results obtained
for the conformal coupling case.
