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At present the possible existence of planets around the stars of a closebinary system is still matter of debate. Can planetary bodies form in spite ofthe strong gravitational perturbations of the companion star? We study in thispaper via numerical simulation the last stage of planetary formation, fromembryos to terrestrial planets in the Alpha Cen system, the prototype of closebinary systems. We find that Earth class planets can grow around Alpha Cen A ona time-scale of 50 Myr. In some of our numerical models the planets formdirectly in the habitable zone of the star in low eccentric orbits. In onesimulation two of the final planets are in a 2:1 mean motion resonance that,however, becomes unstable after 200 Myr. During the formation process someplanetary embryos fall into the stars possibly altering their metallicity.Comment: accepted for pubblication in A&A, 13 pages, 9 figure

Formation of terrestrial planets in close binary systems: The case ofαCentauri A