In Fe3Ga single crystals with the D03 structure, three types of pseudoelasticities based on dislocation motion, martensitic transformation and twinning take place depending on the heat treatment, the loading axis and the stress sense. In this paper, we report the detail of the transformation and twinning pseudoelasticities in the crystals focusing on the crystallography and the temperature dependence. In particular, the driving force for the twinning pseudoelasticity was discussed, focusing on the atomic arrangement. In Fe3Ga single crystals homogenized or solutionized in the α disordered region, the martensites with the 14M structure, containing numerous stacking faults were stress-induced during loading, while they disappeared during unloading by the reverse transformation, resulting in the transformation pseudoelasticity with small stress-strain hysteresis. In contrast, twinning pseudoelasticity caused by twinning and untwinning of 2.2T-type pseudo-twins appeared in the well-ordered D03 crystals, accompanied by a serrated flow in the stress-strain curve. The contribution of the twinning pseudoelasticity to strain recovery became significant at low temperatures at which the dislocation motion was difficult. It should be noted that the formation of the pseudo-twins could be regarded as a certain displacive phase transformation since the crystal structure of the twins became orthorhombic due to the twin shear without atomic shuffling. The free energy difference between the D03 matrix and the pseudo-twins resulted in the twinning pseudoelasticity. Moreover, the pseudo-twins were transformed into the perfect twins by annealing at 300 °C where the atomic shuffling could occur. The perfect twins remained even after complete unloading due to their low driving force for the pseudoelasticity.