We study the effect of a non-vanishing flux for the NS-NS antisymmetric ten
sor 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 Mobius amplitude involves some sign
s that, in the Z(2) orbifold, allow one to connect: continuously U(n) group
s to Sp(n) x Sp(n) groups on each set of D-branes. In this case, non-univer
sal 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 I scenario, wher
e supersymmetry is broken on the D-branes, while it is preserved in the bul
k. (C) 2000 Elsevier Science B.V. All rights reserved.