Mössbauer spectroscopic method has been used to determine the magnetic behavior of Fe-Ni fine particles (≈200 Å) in the concentration range 10 to 35 at% Ni. The Mössbauer spectra of the alloys having 20, 22.5 and 25 at% Ni show the existence of a broad central line (which can be fitted with a Lorentzian doublet) along with a sextet whereas the spectrum of Fe72.5Ni27.5 alloy shows only a broad central line (which can also be fitted with a Lorentzian doublet). The central line in each of the above cases disappears for large particles, suggesting that this line originates from the superparamagnetic behavior of the ferromagnetic fine particles. Mössbauer spectroscopic studies reveal that ferromagnetic order appears in fine particles (≈200 Å) of Fe70Ni30 and Fe65Ni35 alloys. The experimental results suggest that the anisotropy energy changes with the change of Ni concentration in these alloys.