  We review the construction of open descendants of the type IIB superstring on
the Z-orbifold. It results in a chiral four-dimensional model with gauge group
$SO(8) \otimes U(12)$ and three generations of matter in the $(8,12^*)\oplus
(1,66)$ representations. As a test of type I - heterotic duality, that reduces
to a weak/weak duality in D=4, a heterotic model on the same orbifold is also
presented. The massless spectrum reproduces exactly the one found in the type I
case apart from additional twisted matter charged with respect to the SO(8)
gauge group. The puzzle is solved by noting that at generic points in the
moduli space these states get masses.
