Giant magnetoresistance (MR) was studied in alloys of composition Cu80Fe10Ni10, Cu80Fe15Ni5, Cu80Fe5Ni15, and Cu80Fe20, produced by melt spinning and annealed in the temperature range 300–600 °C. Materials were characterized by Mössbauer spectroscopy at several temperatures. At both 78 and 300 K, spectra for all CuFeNi compositions showed a singlet associated with superparamagnetic Fe nanoparticles, but at 4.2 K the sextet characteristic of ferromagnetic Fe was visible. From the hyperfine field reduction we estimated the radius of the Fe particles. Magnetization data for Cu80Fe10Ni10 at 300 K were compared with a model which features a log-normal distribution of noninteracting superparamagnetic particles. Thus the mean magnetic moment and the particle density were determined. The magnetoresistance ratio MR was compared to a model which considers bulk and interface scattering.