The structural, hyperfine, and magnetic properties of mechanically milled alloys of (Fe79Mn21)1−xCux (x from 0.00 to 0.30) have been characterized by x-ray diffraction (XRD), extended x-ray absorption fine structure spectroscopy (EXAFS), Mössbauer spectroscopy, and ac susceptibility measurements. XRD and EXAFS results indicated that Cu addition favored the formation of a Fe–Mn–Cu random solid solution with fcc structure. The lattice parameter exhibited linear dependence on the Cu content, which is compatible with the larger atomic radii of the Cu atoms when compared with the Mn or the Fe ones. The dependence of Mössbauer hyperfine parameters on the Cu content at room temperature is coherent with the formation of a ternary phase. The ac susceptibility curves jointly with the Mössbauer results are representative of a spin-glass-like system.