  In this paper, we study strong symplectic fillability and Stein fillability
of some tight contact structures on negative parabolic and negative hyperbolic
torus bundles over the circle. For the universally tight contact structure with
twisting $\pi$ in $S^1$-direction on a negative parabolic torus bundle, we
completely determine its strong symplectic fillability and Stein fillability.
For the universally tight contact structure with twisting $\pi$ in
$S^1$-direction on a negative hyperbolic torus bundle, we give a necessary
condition for it being strongly symplectically fillable. For the virtually
overtwisted tight contact structure on the negative parabolic torus bundle with
monodromy $-T^n$ ($n<0$), we prove that it is Stein fillable. By the way, we
give a partial answer to a conjecture of Golla and Lisca.
