Effect of ageing conditions (ageing in the high-temperature phase (austenite) in free state and under stress and ageing in martensite under stress, ageing temperature and time) on the development of stress-induced BCC-FCC martensitic transformation (MT) and superelasticity (SE) was studied in the FeMnAlNi single crystals along the [001] direction under compression. It is shown that the precipitation of nanosized particles of the β-phase (ageing in austenite for 3 and 6 h at 473 K in a free state and under stress and ageing in martensite under stress for 3 h at 473 K) leads to an increase in the stress level for the onset of stress-induced BCC-FCC MT σcr and to the creation of crystals with high-temperature SE at temperatures above 373 K. SE is observed in a wide temperature range: from 273 to 473 K in quenched crystals; from 203 to 573 K after ageing in austenite at 473 K for 3 and 6 h in a free state and under stress and after ageing in martensite under stress at 473 K for 3 h. The maximum SE is 6.3–8.3% and 6.2% after ageing in austenite and in martensite under stress, respectively. It was shown for the first time that after ageing in martensite under stress (when transformation strain εtr=3%) for 3 h at 473 K, the SE curves are characterized by two stages, which are not observed after ageing in austenite under stress. The influence of particles on the σcr and the mechanical hysteresis Δσ is discussed.