  We consider the special case of the restricted circular three-body problem,
when the two primaries are of equal mass, while the third body of negligible
mass performs oscillations along a straight line perpendicular to the plane of
the primaries (so called periodic vertical motions). The main goal of our
investigation is to study the stability of these periodic motions in the linear
approximation. A special attention is given to the alternation of stability and
instability within the family of periodic vertical motions, whenever their
amplitude is varied in a continuous monotone manner.
