FePd(001) thin films have been grown by the molecular beam epitaxy (MBE) technique. At room temperature, these films are chemically disordered whereas at 350 °C a well ordered L10 structure is found with the c-axis oriented in the growth direction. By combining RHEED, STM and Auger measurements, it is suggested that ordering occurs at the growing surface by the development of bi-atomic steps of the ordered structure. We have put in evidence that the surfactant behavior of the Pd atoms is mainly involved in the ordering process and selects the single orientation of the c-axis. For intermediate temperatures between RT and 350 °C, TEM and X-rays have evidenced a pseudo-periodic arrangement of anti-phased domains having a columnar shape. The variation of the long-range order parameter is related to the average size of these ordered domains.