Fe films 2-20 atomic monolayers (ML) thick have been deposited on Ni(1 1 1) films (4-60 ML) prepared on W(1 1 0) under UHV conditions. The Ni(1 1 1) films grow in a Nishijama-Wassermann orientation with a 3.6% lattice expansion along Ni[(2) over bar 1 1] (parallel to W[(1) over bar 1 0]). On top of these slightly distorted Ni films iron is observed to grow preferentially in two mirror orientations. The saturation magnetization of these Fe films and the anisotropies of Fe/Ni bilayers have been studied using torsion oscillation magnetometry. The magnetization of the Fe films of 2.13 mu(B) per atom is close to the bulk value of Fe. The out-of-plane surface (interface) anisotropy constant K-s(FeNi) = (- 0.65 +/- 0.15) mJ/m(2) of the bilayers prefers a magnetization perpendicular to the surface. The exceptionally high value of the volume anisotropy constant of the Fe films, K-v(Fe) = (+ 0.71 +/- 0.10) MJ/m(3) = (52.2 +/- 7.5) μ eV/atom, was ascribed to magnetoelastic contributions.