In-plane fourfold and uniaxial magnetic anisotropies were studied in Fe films epitaxially grown on vicinal Ag(001) and Au(001) surfaces, which were prepared by molecular beam epitaxy on miscut GaAs(001) substrates. The effective fourfold and uniaxial anisotropy constants, K-1(eff) and K-u(eff), which are determined from magnetisation curves measured with the magneto-optic Kerr effect, are linear functions of the inverse Fe layer thickness. The fourfold anisotropy shows a rotation of the easy and hard axes by 45 degrees below a critical thickness of 6-7 ML. The uniaxial term is mainly an interface contribution. We find that the orientation of the uniaxial easy axis depends on the Fe thickness. In thinner films (t(Fe) less than or equal to 20 ML) it is oriented perpendicular to the step edges, i.e., parallel to Fe[100]. This excludes shape anisotropy as the main mechanism. Above a critical thickness the uniaxial easy axis is aligned parallel to the step edges, i.e., along Fe[010]. This step-induced uniaxial anisotropy may be due to modified electronic states and to strain from the large vertical misfit at the steps. (C) 1999 American Institute of Physics. [S0021-8979(99)64408-5].