The Fe_xZn_1−xF₂ alloy has been shown to be a model system for studying the magnetic phase diagram of dilute magnets. Whereas the growth of bulk single crystals with fixed Zn concentrations is difficult, the thin film growth is comparatively simpler and more flexible. To gain an understanding of the growth of Fe_xZn_1−xF₂ films, a method was developed to grow smooth films at fixed concentrations. This was done by depositing a MgF₂ buffer layer on MgF₂(001) substrates and then depositing FeF₂ and ZnF₂ [001]-orientated epitaxial thin films at different temperatures. Surprisingly, the lattice spacing depends strongly on the growth temperature, for 44-nm-thick FeF₂ films and 77-nm-thick ZnF₂ films. This indicates a significant amount of stress, despite the close lattice match between the films and the MgF₂ substrate. Thick alloy samples (approximately 500 nm thick) were grown by co-evaporation from the FeF₂ and ZnF₂ sources at the ideal temperature determined from the growth study, and their concentration was accurately determined using x-ray diffraction.