  We study the effect of a non-vanishing flux for the NS-NS antisymmetric
tensor in open-string orbifolds. As in toroidal models, the total dimension of
the Chan-Paton gauge group is reduced proportionally to the rank of $B_{ab}$,
both on D9 and on D5-branes, while the Moebius amplitude involves some signs
that, in the $Z_2$ case, allow one to connect continuously ${\rm U} (n)$ groups
to $Sp(n) \otimes Sp(n)$ groups on each set of D-branes. In this case,
non-universal couplings between twisted scalars and gauge vectors arise, as
demanded by the generalised Green-Schwarz mechanism. We also comment on the
role of the NS-NS antisymmetric tensor in a recently proposed type scenario,
where supersymmetry is broken on the D-branes, while it is preserved in the
bulk.
