Nickel-free Co-Cr-W-Mo alloys exhibit a very low or even negative stacking fault energy, and therefore a pronounced tendency towards a deformation-induced phase transformation of the metastable face-centered cubic (fcc) γ-phase to the hexagonal close-packed (hcp) low-temperature ε-phase. In order to analyze the phase transformation in-situ and to correlate it to an external strain, compression tests between 30 °C and 400 °C were performed in a deformation dilatometer simultaneously to high-energy X-ray diffraction. Hence, the elastic strains of the fcc unit cell during compression, the external loads for the onset of the phase transformation and the temperature-dependency could be determined. In the parent fcc γ-phase, the evolution of an 101 fiber texture as well as texture inheritance effects and a distinct variant selection could be observed. Further, for the investigated alloy composition it is demonstrated that the continuum concepts of i) a structural stretch tensor and ii) an invariant plane strain perfectly agree with the widely-accepted nucleation theory of ε-martensite formation in Co-Cr alloys via Shockley partial dislocations on every second {111} _γ plane. Both, the observed transformation texture as well as crystallographic transformation strains reveal the importance of shear stresses in this system.