We present new studies of the pressure effect on the stability of the ferromagnetic (FM) state in fcc Fe-based alloys up to 8 GPa and at different temperatures (300-2 K) using the 57Fe high pressure Mössbauer technique. The selected systems include weak (Fe 68.3Ni 31.5) and strong (Fe 72Pt 28) itinerant ferromagnets. We find in both weak and strong ferromagnets a pressure-induced magnetic phase transition from the FM, high-spin (HS) state to a low-spin (LS) state at a critical pressure. The existence of two energetically close lying magnetic states (HS and LS) reveals a unique physical picture of ferromagnetism in fcc Fe-based systems that exhibit large magnetovolume effects. The results are compared with spin polarised band structure calculation of fcc Fe. Differences between the behavior of weak and strong ferromagnets are also discussed.