  This paper investigates the long-term orbital stability of small bodies near
the central binary of the Alpha Centauri system. Test particles on circular
orbits are integrated in the field of this binary for 32000 binary periods or
approximately 2.5 Myr. In the region exterior to the binary, particles with
semi-major axes less than roughly three times the binary's semi-major axis are
unstable. Inside the binary, particles are unstable if further than 0.2 binary
semimajor axes from the primary, with stablility closer in a strong function of
inclination: orbits inclined near 90 degrees are unstable in as close as 0.01
binary semimajor axes from either star.
