  We consider non-perturbative six and four dimensional N=1 space-time
supersymmetric orientifolds. Some states in such compactifications arise in
``twisted'' open string sectors which lack world-sheet description in terms of
D-branes. Using Type I-heterotic duality we are able to obtain the massless
spectra for some of such orientifolds. The four dimensional compactification we
discuss in this context is an example of a chiral N=1 supersymmetric string
vacuum which is non-perturbative in both orientifold and heterotic pictures. In
particular, it contains both D9- and D5-branes plus non-perturbative
``twisted'' open string sector states as well.
