  We study the nature of the instability of the homogeneous steady states of
the subcritical Ginzburg-Landau equation in the presence of group velocity. The
shift of the absolute instability threshold of the trivial steady state,
induced by the destabilizing cubic nonlinearities, is confirmed by the
numerical analysis of the evolution of its perturbations. It is also shown that
the dynamics of these perturbations is such that finite size effects may
suppress the transition from convective to absolute instability. Finally, we
analyze the instability of the subcritical middle branch of steady states, and
show, analytically and numerically, that this branch may be convectively
unstable for sufficiently high values of the group velocity.
