  The Casimir-Polder force between two atoms with equal uniform acceleration
and separated by a constant distance R is considered. We show that, in the
low-acceleration limit, while the near-zone R^{-6} behavior of the interatomic
interaction energy is not changed by the acceleration of the atoms, the
far-zone interaction energy decreases as R^{-5} instead of the well-known
R^{-7} behavior for inertial atoms. Possibility of an indirect detection of the
Unruh effect through measurements of the Casimir-Polder force between the two
accelerating atoms is also suggested. We also consider a heuristic model for
calculating the Casimir-Polder potential energy between the two atoms in the
high-acceleration limit.
