D0(3)-ordered Fe3Al single crystals containing 23, 25 and 28at.%Al were cyclically deformed at [149] loading axis in tension-compression mode. Giant pseudoelasticity took place in Fe-23 and 25at.%Al single crystals at an early stage of cyclic deformation, while a slight strain recovery was observed in Fe-28at.%Al. In Fe-23 and 25at.%Al single crystals, superpartial dislocations with Burgers vector of 1/4[111] moved individually dragging the nearest neighbour anti-phase boundary (NNAPB). The NNAPB pulled back the superpartials during unloading, resulting in giant pseudoelasticity and low residual dislocation density. In contrast, a couplet of the superpartials was observed to bow out leaving two superpartials in Fe-28at.%Al. This means that the dislocation couplet dragged the next-nearest neighbour anti-phase boundary (NNNAPB). The surface tension of NNNAPB is lower than that of NNAPB resulting in a slight strain recovery in Fe-28at%Al. As cyclic deformation proceeded, residual dislocation density increased with an increase in the number of cycles even in Fe-23 and 25at.%Al. In particular, persistent slip bands (PSB) were formed in Fe-23at.%Al single crystals, though PSB is seldom observed in fatigued intermetallic compounds. To-and-fro motion of superpartials during loading and unloading was suppressed by dislocation bundles, resulting in a reduced shape recovery. However, large strain recovery occurred in Fe-25at.%Al single crystals at a strain amplitude of 1.0% even at 20cycles. It was also noted that Fe-23 and 25at.%Al demonstrated tension-compression asymmetry even at [149] orientation; the yield stress in compression was higher than that in tension. This implies that the core structure of < 111 > screw dislocation played an important role in the deformation behaviour of Fe3Al single crystals.