  It is well established that certain detached eclipsing binary stars exhibit
apsidal motions whose value is in disagreement with with calculated deviations
from Keplerian motion based on tidal effects and the general theory of
relativity. Although many theoretical senarios have been demonstrated to bring
calculations into line with observations, all have seemed unlikely for various
reasons. In particular, it has been established that the hypothesis of a third
star in an orbit almost perpendicular to the orbital plane of the close binary
system can explain the anomalous motion in at least some cases. The stability
of triple star systems with highly inclined orbits has been in doubt, however.
  We have found conditions which allow the long term stability of such systems
so that the third body hypothesis now seems a likely resolution of the apsidal
motion problem. We apply our stability criteria to the cases of AS Cam and DI
Her and recommend observations at the new Keck interferometer which should be
able to directly observe the third bodies in these systems.
