The atomic structure of Fe–Al (7 and 9 at % Al) and Fe–Ga (18 at % Ga) alloys is studied by X‑ray diffraction using a laboratory four-circle diffractometer. After refining annealing, single-crystal alloy samples were annealed in the ferromagnetic state ( T < T _C). One sample of the Fe–18 at % Ga alloy, after short holding in the paramagnetic state ( T > T _C), was quenched in room temperature water. Earlier, the authors reported on the peculiarities of the ordering of alloying atoms in B 2 and D 0_3 phase structures in quenched and annealed samples of these alloys. Here, we present and discuss the results of our observations in these alloys of a new phase with a face-centered cubic (fcc) lattice ( B 1-type structure with NaCl prototype and unit cell parameter ~5.2 nm). The fcc phase appears in the Fe–Al alloy as the aluminum concentration increases from 7 to 9 at %; it is observed in the Fe–18 at % Ga alloy, and its volume fraction increases after annealing in the ferromagnetic state in comparison with a quenched alloy sample. In these alloys (9 at % Al) and (18 at % Ga), different ways of embedding fcc crystals in the bcc phase of single crystals are realized; i.e., the axes of the fcc lattice are directed in four different ways relative to the axes of the bcc lattice.