  At present the possible existence of planets around the stars of a close
binary system is still matter of debate. Can planetary bodies form in spite of
the strong gravitational perturbations of the companion star? We study in this
paper via numerical simulation the last stage of planetary formation, from
embryos to terrestrial planets in the Alpha Cen system, the prototype of close
binary systems. We find that Earth class planets can grow around Alpha Cen A on
a time-scale of 50 Myr. In some of our numerical models the planets form
directly in the habitable zone of the star in low eccentric orbits. In one
simulation two of the final planets are in a 2:1 mean motion resonance that,
however, becomes unstable after 200 Myr. During the formation process some
planetary embryos fall into the stars possibly altering their metallicity.
