Single-phase, bcc Fe(Ag) alloy thin films were prepared in the concentration range from 0 at. % to 40 at. % Ag by pulsed laser deposition from elementary Fe and Ag targets onto Si(111) substrates cooled to 150 K. The peaks in x-ray-diffraction patterns are rather sharp and indicate coherence lengths between 7 nm (at 40 at. % Ag) and 30 nm (at 10 at. % Ag). The nonequilibrium phase is stable up to 450 K and decomposes above this temperature: Fe nuclei form inside the nonequilibrium phase and grow, leaving many Ag atoms in a noncoherent arrangement in the grain boundaries.