Fcc Fe-Co alloy films (1.5-9 monolayers) were prepared on Cu(001) by epitaxial deposition at room temperature. Growth, structural and magnetic properties of these films were investigated by medium- and low-energy electron diffraction, Auger electron spectroscopy, as well as magneto-optical Kerr effect measurements. Addition of Fe in the fcc Co films results in an uneven vertical expansion of a part of the alloy films, its extent depending on composition. For more than 70 at.% Fe, essentially the whole film is vertically expanded, which is accompanied by a change of the growth mode and the appearance of some uniaxial structural irregularity in the plane of the films. The easy axis of the magnetization was found to lie within the film plane over the whole range of compositions for the investigated thicknesses. A linear increase of the Kerr signal at saturation magnetization with increasing thickness indicates that the whole alloy film is magnetic. A constancy of the Fe and Co local magnetic moments can be expected below 70-80 at.% of Fe.