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The effect of high pressure and ion beam irradiation on the magnitude of giant magnetoresistance (GMR) of Fe/Cr magnetic multilayers (MML), [Fe(20 Å)/Cr(t Å)]20 (abbreviated as Fe/Cr(t)), has been measured at 77.4 K. It is found that the GMR of Fe/Cr(8) is decreased but that of Fe/Cr(30) is increased by applying pressure. By ion beam irradiation, the electrical resistance of these MMLs is increased significantly and the magnitude of GMR is decreased. Furthermore we have measured the GMR of irradiated Fe/Cr(8) and Fe/Cr(30) under high pressure and compared the results with the sample before irradiation. The GMR of Fe/Cr(8) after the irradiation is found to increase with pressure and the pressure-coefficient of the saturation resistivity is extremely large. These results are discussed on the basis of the spin dependent scattering by the roughness at the interfaces and also bulk scattering in MML in connection with an irradiation-induced instability of the electronic states in Fe/Cr(8).