We have grown single-crystal (001) epilayers of the diluted magnetic semiconductor Zn1−xFexSe on GaAs(001) substrates by molecular beam epitaxy. The films were characterized with Auger electron spectroscopy (AES) and reflection high-energy electron diffraction, followed by x-ray θ–2θ, rocking curve, and topography measurements. AES data show that the surface stoichiometry does not change significantly under electron beam exposure, indicating that (Zn,Fe)Se is a more stably bonded compound than (Zn,Mn)Se, where large variations are observed. The variation of the lattice parameters both parallel and perpendicular to the surface is obtained as a function of Fe concentration. The Zn1−xFexSe epilayers are cubic in structure for x≤0.22 and thicknesses up to at least 2 μm, although films with x>0.05 exhibit a slight tetragonal distortion (1≤c/a<1.002). The onset of this distortion is reflected in a broadening of the x-ray double-crystal rocking curve. Dislocation densities obtained from the rocking curve linewidth range from 1 to 7.5×108 cm−2. X-ray topographs reveal a degree of mosaic structure which increases with Fe content.