  In this paper, we will define the reduced cross-sectional $C^*$-algebras of
$C^*$-algebraic bundles over locally compact groups and show that if a
$C^*$-algebraic bundle has the approximation property (defined similarly as in
the discrete case), then the full cross-sectional $C^*$-algebra and the reduced
one coincide. Moreover, if a semi-direct product bundle has the approximation
property and the underlying $C^*$-algebra is nuclear, then the cross-sectional
$C^*$-algebra is also nuclear. We will also compare the approximation property
with the amenability of Anantharaman-Delaroche in the case of discrete groups.
