The study at low temperatures of powder of the Invar alloy, Fe67.5Ni32.5, produced by mechanical alloying, shows that the sample presents two structural phases, the Fe-Ni BCC and the Fe-Ni FCC. The 57Fe Mössbauer spectra obtained in this sample at different temperatures were fitted considering two hyperfine magnetic field distributions. The first one having the larger mean field and only one peak (at ca. 35 T, varying with T), is associated with the BCC phase, and the second one, presenting several broad peaks (distributed between 10 and 35 T), is associated to the FCC phase. A singlet, which is associated to low spin Fe sites of the FCC phase, was also considered. The mean hyperfine magnetic field of the BCC phase increases monotonically as temperature decreases, while that of the FCC phase presents an anomaly near 75 K. The real part of the ac magnetic susceptibility temperature scans presents a peak whose position increases from 31 to 39 K, when the ac field frequency increases from 100 to 5000 Hz. These results permit to associate the detected anomaly to the occurrence of a reentrant spin glass transition. © 2015 Elsevier B.V. All rights reserved.