Polytetrahedral NiFe nanoparticles with diameters of (2.8+/-0.3) nm have been obtained by hydrogenation of Ni[(COD)(2)] (COD=1,5-cyclooctadiene) and Fe[{N(SiMe(3))(2)}(2)] at 150 degrees C using stearic acid and hexadecylamine as stabilizing ligands. The nanoparticles are superparamagnetic at room temperature and display a blocking temperature of 17.6 K. Their anisotropy (2.7x10(5)J m(-3)) is determined to be more than two orders of magnitude higher than that of the bulk NiFe alloy (10(3)J m(-3)) and is close to that determined for Fe nanoparticles of the same size. Still, they display a magnetization of (1.69+/-0.05) mu(B) per metallic atom, identical to that of the bulk NiFe alloy. Combining the results from X-ray absorption and Mössbauer studies, we evidence a progressive enrichment in iron atoms from the core to the surface of the nanoparticles. These results are discussed in relation to both size and chemical effects. They show the main role played by the enriched Fe surface on the magnetic properties and address the feasibility of soft magnetic materials at the nanoscale.