Deformation mechanisms, one-way and two-way shape memory effects were studied in the mode of compression in the [011] single crystal of the Ni₅₅Fe₁₈Ga₂₇ alloy where the detwinning occurred during deformation and in the [001] single crystal where the detwinning was forbidden. It was found that the [001] and [011] crystals deformed by different mechanisms during compression to 5% (reorientation was in [001] crystal, and the reorientation and detwinning were in [011] crystal) and from 15 to 20% (the 14 M → L1₀ transition was in [001] crystal and plastic deformation of 14 M phase was in [011]). The compression of both single crystals from 5 to 15% occurred due to the same mechanisms: the 10 M ↔ 14 M transformation and the plastic deformation of the 14 M martensite. The 14 M and L1₀ phases were stable under load, and they transformed to the 10 M martensite on unloading. It was shown that the crystal orientation and detwinning hardly affected the value of the one-way shape memory effect since both crystals were in the 10 M martensite after preliminary deformation. In this case, the transformation of 10 M martensite to the austenite on heating was accompanied by a strain of about 5% and this was the maximum value of the shape memory effect. It was found that the detwinning significantly affected the temperature ranges of strain recovery. In the [011] crystal, the strain recovered in a very narrow interval on heating (1-2°C), whereas in the [001] crystal the shape memory effect was observed in “normal” temperature range (~ 10°C). The detwinning resulted in the formation of a large oriented internal stress during the preliminary deformation that increased the value of the two-way shape memory effect that was observed in [011] crystals in comparison with the [001] crystals.