Electron transmission microscopy was done on the Fe alloys with 29.8 and 37.2 at.% Mn. with the γ→ε{lunate} transformation induced by all three driving forces: temperature change, cold deformation and high-pressure soaking (up to 9.0 GPa (90 kbar)). Contrary to the well established data, the presence of the ε{lunate} phase after cooling was observed at Mn concentrations not less, than 37at.%. It was proved by direct observation that high-pressure soaking and cold deformation strongly affect phase equilibria in Fe-Mn alloys: this effect is dependent on the Mn concentration, decreasing with it. The familiar orientation relationships between γ and ε{lunate} phases, namely (1̄11)γ ∥(0001)ε{lunate}, and [101̄]γ ∥[112̄0]ge, are observed in all obtained structures independently of the kind of driving force applied to promote the γ→ε{lunate} transformation. It is proposed to explain the unusual behaviour of Fe-Mn alloys (limited growth of the ε{lunate} martensitic phase upon cooling in the vicinity of Mγ→ε{lunate}s. very small sizes of the ε{lunate} particles) by a model which takes into account the antiferromagnetic ordering in both phases. It is shown that this explanation is consistent with experimental results. © 1979.