Orientifolds of the type IIB superstring that descend from F-theory an
d M-theory orbifolds are studied perturbatively. One finds strong evid
ence that a previously ignored twisted open string is required in thes
e models. An attempt is made to interpret the J-type torsion in F-theo
ry where one finds a realization of Gimon and Johnson's models which d
oes not require these twisted strings. S-duality also provides evidenc
e for these strings.