X-ray diffraction and electron microscopy were used to study the development of the γ-ɛ martensitic transformation (MT) upon tensile deformation of single crystals of (I) the Fe-17% Cr-12% Ni-2% Mn-0.75% Si and (II) Fe-18% Cr-12% Ni-2% Mo-0.015% C (wt %) austenitic stainless steels as a function of the crystal-axis orientation and the test temperature T. It has been shown that a decrease in the test temperature to T<173 K in single crystals of steels I and II with a low stacking fault energy (γ0=0.01–0.015 J/m2) leads to a γ-ɛ-α’ MTs upon plastic deformation. It has been established that the degree of deformation preceding the γ-ɛ MT depends on the crystal-axis orientation and the γ0 magnitude. In the [011] and \([\bar 1 11]\) crystals, the γ-ɛ MT upon tension is developed already at early stages of plastic flow, at ɛ≤3%, whereas in the \([\bar 1 23]\) and [012] crystals it occurs after a substantial deformation by slip, at ɛ=16–70%. In the [001] crystals, no γ-ɛ MT is revealed by X-ray diffraction, but 1–2% ɛ phase is observed by electron microscopy. The physical cause for the observed orientation dependence in the γ-ɛ MT is related to the effect of external stresses σ on the degree of splitting of perfect dislocations a/2〈110〉 to Shockley partial dislocations a/6〈211〉, which form nuclei of the ɛ phase.