  In this paper we consider compactifications of type I strings on Abelian
orbifolds. We discuss the tadpole cancellation conditions for the general case
with D9-branes only. Such compactifications have (perturbative) heterotic duals
which are also realized as orbifolds (with non-standard embedding of the gauge
connection). The latter have extra twisted states that become massive once
orbifold singularities are blown-up. This is due to the presence of
perturbative heterotic superpotential with couplings between the extra twisted
states, the orbifold blow-up modes, and (sometimes) untwisted matter fields.
Anomalous U(1) (generically present in such models) also plays an important
role in type I-heterotic (tree-level) duality matching. We illustrate these
issues on a particular example of Z_3 \otimes Z_3 orbifold type I model (and
its heterotic dual). The model has N=1 supersymmetry, U(4)^3 \otimes SO(8)
gauge group, and chiral matter. We also consider compactifications of type I
strings on Abelian orbifolds with both D9- and D5-branes. We discuss tadpole
cancellation conditions for a certain class of such models. We illustrate the
model building by considering a particular example of type I theory
compactified on Z_6 orbifold. The model has N=1 supersymmetry, [U(6)\otimes
U(6)\otimes U(4)]^2 gauge group, and chiral matter. This would correspond to a
non-perturbative chiral vacuum from the heterotic point of view.
