  We consider non-perturbative four dimensional N=1 space-time supersymmetric
orientifolds corresponding to Type I compactifications on (generalized)
Voisin-Borcea orbifolds. 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 as well as the map between Type IIB
orientifolds and F-theory we are able to obtain the massless spectra of such
orientifolds. The four dimensional compactifications we discuss in this context
are examples of chiral N=1 supersymmetric string vacua which are
non-perturbative from both orientifold and heterotic points of view. In
particular, they contain both D9- and D5-branes as well as non-perturbative
``twisted'' open string sector states. We also explain the origins of various
inconsistencies arising in such compactifications for certain choices of the
gauge bundle.
